Okay here we go. Green is for go. City Council discussion item number one the commercial retention and redevelopment CRR program formerly known as the facade program and we'll have Ms. Ayesha Dreggers our Director of Office of Business Opportunities. Good morning everyone. It's great to see y'all this morning. I also have our staff here Brett Whiting and Carla Eichelberger those are the staff members responsible for our commercial retention and redevelopment program that was formerly the facade program as people are familiar with it with that title. So I just want to provide you with some updates we didn't have funding last fiscal year but we do this year so we're excited to get kicked off with that program. All right so here's an overview of the program we offer 15,000 for exterior improvements and 10,000 for the interior improvements and then we also have an additional incentive for vacant or abandoned buildings for $10,000. The property must be vacant for 12 consecutive months prior to those improvements and that's just an incentive to kind of fill vacant spaces. That was started a couple years ago in the five-point area. It has been yes. So eligible businesses you can be a property owner or a tenant of the business to participate in the forgivable loan and the tenants have to get approval from the property owners in order to apply for that. I did want to point out the ineligible businesses listed here. The residential use of course, government, public educational facilities, franchises, hotels, liquor stores, convenience stores, private education chain stores, businesses with 51% are more of revenue from alcohol sales and adult-oriented businesses are ineligible for participating. So this is the question that I had because we do have businesses that are restaurants but then also serve alcohol and five points and I know we had a conversation via email about how there's no federal restriction or program restriction and that is maybe a OBO or OBO law. Oh, it's a Tina Herbert rule. That was started during my, because we had a lot of five-point bars that had issues with that arose out of alcohol incidents and we just say bar versus restaurant. Yeah because there are some restaurants that I think should qualify but well and that's how we determine what qualifies. If you... It's 51%.  No, we're a restaurant because we serve food. So I'm sorry that is the background to that. Okay. The legal cases that have come out through the Parpoolian law firm, I believe they use 35% as a threshold for alcohol sales. No, for food sales. You have to have at least 35% of your income off of food in those cases where some of the bars shut down. And I think our standards should be higher because we're talking about businesses that we are investing in. Descartes-Potlian is not talking about investing in. Well that's the thing like this is when you're looking at it holistically you want to be able to invest in an area to make it look better. That's the whole point of the program so I don't want to make it harder. I do think we should be intentional and not be you know using it for something that will turn over in you know two years because it's just a bar but there I do feel like so something like Jake's with that does serve 50% or more but people also eat there right so they would be ineligible and that's just one example but I do think that there are I just want to make sure that there could be conversations about I'm thinking even different than that because let's say you have a high end tapas okay that goes into five points and they're taking over an old building and they want to go in it well if you go in there and you get a $75 bottle of Cabernet and you and Aliana split an entree well it's a lot more than 50% spent on alcohol but it's it's a restaurant I think we got to have some leeway that's what I'm at yeah let's accept one well I mean I would have to go to the list but I think we did find when we did it previously I don't know high end stores were necessarily interested in government money as well I had met anybody that's gonna not take a $15,000 facade grant I've already said I've already said this to my guy technologies I mean that is the history of it is that I don't know what the discussion is was to just is that this discussion today no I asked to just get an overview of it because I had some folks ask if they could be eligible for it and based on this we were not so I wanted to know the history of how this rule was created because it's not in the program or federal language that restricts from being able to use it so which I'm fine I just think that there should be some flexibility to allow for that's my stance is there's going to always be you know businesses worth investing in that may not fit squarely in this rule but could make a huge difference when it comes to a particular entertainment district or neighborhood I'm just thinking about like if you go down there and you look at who said it's been empty now for three years it's gonna need a facade grant for somebody to get to go in there along with the other pieces and the people who have been traditionally looking at it oyster bar this and that they're gonna be they could be tucked in there on sales I mean I would argue that today you know probably some of those places if you go back to years ago in five points the majority of places were restaurants but then they turned into bars that later on will that change their whole you know percentage of sales what if they're what if they're 49 we're gonna take somebody for 2% I just I'd like to give staff autonomy I wouldn't give staff autonomy because I think you get them in trouble I think if a company applies and they have more than 51% sales from beer alcohol that's the viewer will have it alcohol and council needs to approve it I would not put that in city staff's hands I'm fine with that I just want the ability to have that flexibility what's the other part of today's discussion that I was hoping outside of the overview and addressing this is that they certainly have interest because we've already there I guess before knowing that we wanted to do the overview and get some of this clarification the staff has softly put out the fact that we do have funding this year so they have gotten started getting interest about it and so some of the history I wanted I should also give was about over the years there's been iterations of we're gonna focus in one corridor and we want to focus on I think at one point we were targeting certain types of establishments to focus on to improve the barbershops and so in the targeted areas I think is where we were we're still yeah you need some direction and we need direction on is are we doing citywide are we saying in our targeted area and that's well and I do have a slide on that and I will share that we did work with Krista's group and we've identified there about 12 bars in the five points area so there is limited funding as well and since bars have been told no for the past probably 10 years we anticipate if we say yes then we'll probably have you know an increase of interest from not interested in bars I'm interested in restaurants that's right yeah so it's how we defined how we define that and if we use the 51% definition to determine if they are considered I think we decided that we accepted and then if there's one that that city council helps make that make that decision that would it be better to instead of using alcohol use food like the law suits do we not the law suits I think as a dip they're not comparable standards this is the city government investing in a business that sells alcohol totally different than dick's law suits and the because and honestly you wouldn't want to tie because he is showing how the bars are problems and and so you wouldn't want to tie your philosophy wouldn't be there do you something like you would have maybe developed a language saying like certain businesses you know over there so that's not a this year we're accepting applications but it'll be up to city councils I tell you what's not on there that needs to be on their vape shops I agree with that so we're clear you're suggesting that we take out the language businesses of 51% or more of revenue from alcohol sales no we keep it but if we have one that staff deems there's one that's teeter-tottering that makes sense for us to do that they bring it to council and council approves it so it doesn't put the burden on staff is what how would they happen how I mean I think they're gonna you gonna have restaurants or something I mean yeah I guess that's the thing like I'm like they won't be able to apply if that's in there so and this discretion so what would that look like when we need when judgment calls have to be made you wanted to come to the whole council you wanted to come to a committee of council you want to I definitely don't want it to be put that the staff in that position I don't either but I'm trying to help facilitate what it looks like but I mean if that's the direction we're going and what you can do is we can add you can appeal and a decision like if you deny because of okay first of all you're a new business you can't you can't disqualify them number one if it's a new restaurant you can't disqualify them because you got no sales history yeah no but they're gonna have three years of projections and it's gonna be in a restaurant business for 20 years I'm gonna tell you I can't tell you one year I had a lot of alcohol sales and one year I didn't have a lot of alcohol sales it all depends I mean they can't even make that decision without having the information so every they have to have three years projections what are we really trying to make the distinct the distinction between the restaurant a bar I mean I think I think if we can come up with yeah it's a restaurant in other words if you're a bar then then you probably not going you're not shouldn't go to the appeal process if you're a restaurant then I think we want 50% I just think it's hard when I started thinking about some high-end stuff coming in and there was an example of a certain elected official who might be a lawyer who somebody brought his receipt from his dinner that he had and his alcohol exceeded his meal and it was 75-25 and the point was is that doesn't always work they weren't they weren't submitting the alcohol portion for reimbursement were they well I always just advised that if we establish something we need to be clear about what we're establishing there's no point to put something out there or take something out and then we get into a pattern with bars and or restaurants applying and and then we say no so they're like why what is the city really doing why are you even with oh could you increase the threshold well just one suggestion can we not try and figure it out today and go do some research like naceco's I'm assuming there are some official definitions of what is a restaurant somewhere like Nate Nate calls the looking look at a sure that maybe get some information said businesses with out revenue from alcohol sales are subject to further review and extra other information or something I mean we don't have to make a decision today but thinking something along that lines that way you're not saying no but you're also not saying yes business license may be able to give you the answer to that how they are registered with the naceco so they have a different one yeah yeah that's that's good and I mean you and you can also create another category we don't they don't just think where it's like subject to additional review like it could be like its own yeah we can another thing I talked to missy about is we probably want to look at any nuisance complaints just trying to figure out what any trickle down effect of allowing you know I think that that is actually incumbent that you check nuisance complaints now we would expect cold violations because it's for exterior of it and that that was kind of like the original intent was help deal with the code it was yeah cold violations but and then we all agree shops add those right yeah yeah this is a list of eligible improvements for the interior so with the typical walls things that can't be easily removed and taken to another location and then the exterior the awnings commentary lighting masonry signs as a big one for our businesses improvements on their signage and then signage is a big one the awnings are really expensive call this expensive painting I do have some pictures to the majorities from the outside exterior versus interior I think so yeah but I think what we determine is we did a lot of improvements in the past on the exterior and then if you go inside it's not very aesthetically appeasing so you wanted to do some types of improvements on the inside as well and these are two different grants yes there's an exterior and an interior okay depending on the need because everyone may not need some interior improvements I don't need to be technical but a parking lot is not interior right you're right and are they able to get but one one business can up to a certain amount of funding yeah so they can have one but it can be interior and exterior combined yes we do remind me because I'm drawing a blank you require x amount from the owner as well is it equal match during COVID we we pause that that match in the past it was 20% currently there is no match right now but we have done 20% in the past 20% of the overall cost right they're doing an equal amount of work 20% of the cost some type of improvement I think you got to have something in there do you feel like 20% was well received by that's a little bit difficult for some of our our smaller businesses um but I mean I think they met that requirement in the past I don't know from staff if they've heard any feedback on that 20% um on the commercial side or on the facade side because we're talking about two different lines yeah on the facade side with 20% was required on the facade side on the exterior the interior did not have that requirement so I know from the different sectors that we work many of the businesses in certain corridors are unable to participate because of that 20% um I'm so sure that's an issue I mean I think you got to have a general rule so the question becomes if you make these improvements I mean signs can be taken awnings can be taken lighting can be taken doors and windows can be taken so I guess the question is is you want to make sure that if we're investing in that business maybe maybe it's not 20% cash that they come up maybe it's improvements that equal that amount so that everybody's invested together does that make sense yeah was an incentive for the businesses to participate let's face it many of the improvements that we've done yeah that also don't want to I also don't want to prohibit business especially when we're talking about some of the gateways that need that extra push from you know Brett for some reason I knew that was coming I was seeing how long he was gonna go before he reached 11 the last time we did the program in five points and I'll just point out a business on saluta the gourmet shop they replaced the awning over there and if you know the gourmet shop that awning goes spans almost a half half of the block so our 15 percent I mean I'm sorry our 15,000 was a portion of what the requirement was there and the owner you know participated and added whatever funding was needed and that is true of most of the program programs that we do so based on history is there a way for us to just ensure that they're making investment alongside of us without making it a dollar amount requirement you know and to me like so let's say we're on North Main at the North Main Plaza for example we're the one that further out near I-20 somebody goes in there and we get them a facade grant but they also they're converting to a restaurant so we're helping them with the grease trap could then I guess you could say that grant count is I you know what I want to make sure is that that people are investing for the success all the way around and it's not just well I got this and then all of a sudden three months later right yeah um I think later on in the presentation uh Aisha will go over some some numbers and the numbers will show uh their private investment I just want to confirm do we still have the requirement with the facade that they have to stay in that location a certain number of years for it to be forgiven right it's it's a two year on both sides on the interior and the exterior two years because it's forgivable it's forgivable over two years it used to be forgivable for five years that might have been yeah now that that changed when I came on I don't remember the five so there is a one rule um so yeah we can add some language in there about um in kind and other investments um for the project the grant is so small they they wouldn't buy it they would almost have to put in a whole lot more money and count that towards it but that way it it's the overall investment yeah yeah and this is just a pie chart of the investment since the program started are some iteration of the program since 1997 it's been called different things but there's been a 2.2 million dollar investment with different funding sources I will say um largely over the past 10 years it's mostly been cdbg funding is how we funded um the program and I do have some additional information because this year we do have the addition of the ARPA funds for that is that somebody had mentioned um not too long ago that there was a lot of funding either through sba or treasury for small businesses that you heard no I'm not familiar with what that would be um for for health with growth um for equipment purchases and other other items for businesses um it may be worth reaching out to rick wade at chamber to ask him about because I think it was he that mentioned it to me a couple weeks ago and I'm trying to follow up with him but all I got was a full voicemail okay yeah I'll reach out to see what else I can find you know I should too can I add will you I think this is one good thing we used to do but we would have public investment oh I have so on this slide and this is kind of the one that Brett alluded to over the years the different areas that we've been in and the private investment for each year I will say currently we're in the five points area now we did not have funding last year so we don't have any projects from last year um cdbg does require that we are in a target area because we do have to do an environmental um but as I mentioned we do have ARPA funds available now that um will allow us to extend outside those areas um I probably have about 11 businesses so far that are interested in north main lady street to notch road there's a lot of interest outside of five points while we still need to have a target area I think there is an argument for us extending it with the ARPA funds because we have the flexibility to do so how much is the ARPA funds I'm sorry from the yes um so I have 350 000 for the next two fiscal years so this year 350 and then next year 300 and that's in addition to these two loans that's that's in addition to this program so that would be yeah but we would model that program after the one where we utilize the cdbg dollars okay I think you I think you try to to spread it as best you can yeah I don't know well now that so welcome to the team of world yeah they should see her face she's like this is my but no so here's the issue that we've had we if you try and want if you want people to really see the impact you have to really concentrate all of the improvements in a certain area if you want people to see it um and so that's that's how downtown looks so much different but then when we did north main people still don't even know we did it and that's because we had an eight mile stretch so that's the only reason why I say um it is good to have a targeted area so that people can see the impact of the investments that we're making and I'm not I'm not here for one or the other I just wanted to make make sure to know that that has been our experience and I think along with that which you know the fiscal years have ebbed and flowed over when we could fund the program substantially so that works well when you know that we're sustaining the program year after year year over year because then you can expect to see okay we're going to we've done this in this quarter and we're moving to the next quarter or we're continuing to work in this quarter so you do there were years where back to back you know there was certainly impact and you know a lot of press about main street when the program was used that way but you know that would have to be something during budget time that we're really focusing in on that we're going to continue to invest in the program consistently I mean I do have a couple of pictures of the different areas we've been so we have been in the main north main corridor in the past and you can see there is a you know significant difference in the before and after we've also been Hardin Street North Millwood Taylor Street survey and five points is where we were most recently I think Ms. Herbert I think you were trying to figure out gourmet shop that's the this one right here is gourmet shop awning that right was talking about how long it is that so those awnings can be pretty expensive and during COVID there were a lot of supply chain issues so we experienced that a lot with this project but we were able to expend those CDBG dollars before the deadline which is always good and then I just wanted to we kind of already talked about this the different funding sources because sometimes that matters with how we implement the program where the funds are coming from so currently we have 250,000 from CDBG they must meet a national objective and that one is the to eliminate slum and blight and then there are federal regulations that apply such as the environmental we have to do Davis Bacon interviews with the employees that are on site then with American rescue there we are not limited to our targeted area but the small businesses have to demonstrate that they've been negatively impacted by the pandemic are located in a qualified census tract so those are items that we'll put on the application and make sure we're meeting the requirements of the ARPA funding and then I just have a note about the increase kind of gives you the guidelines right you can actually go with it yes so we'll include that as a part of the application their address and make sure they're within the qualified census tract or a reduction but like I said we have at least 11 that are interested and we really haven't done a full push to say you know the funding is available so I think there's a lot of interest throughout our entire city for this program even the eligibility of being in a qualified census tract is probably not going to be that difficult no and I mean so well I mean it's interesting where those pockets lie it's not sometimes where you think that's what I'm saying so if we to the discussion of if you're going to target it or not I mean I think checking that box is not that difficult we might be surprised where it's a qualified census tract after all so yeah I've looked at some of the ones from the 11 that we've received interest in and they are located in the census tract do we send you businesses that we think might be interested yes yeah I have already received some so um and then our staff will also go out into the community um Brent and Carlett going door to door and five points to determine interest in that area so we'll extend it to other areas in the city if that's the decision that we made to do a citywide program are we doing are we part of any of that that's going on at the other side of the trestle where those folks are redoing the facades not yet but there's been some interest because we're not that's not a targeted area but if we go citywide um we have met with um some of the individuals over there and they are interested what they've done is fabulous it is what is currently the targeted area five points is where we are with the cdbg dollars yes which was it was last year as well right yeah year before last we didn't have any funding last year might be time to switch areas so forgive me total funding for the next two years for this program nine hundred and fifty thousand dollars if we combine our ARPA funding with the cdbg funding when do we decide the path forward on we've cut it up into an equal amount for four districts yeah well cdbg since that application has already been approved that is the target area is five points for the cdbg dollars and those have to be expended by i'm pretty sure april or may so that's the two two hundred and fifty thousand so yeah so so that's that's our priority right now is getting those funds um spent but um i think we had to 2025 to um i'm looking at missy kaufman 2025 or 2026 to expend those 2025 okay if that's the goal we'll do 2025 i feel like that that's it like you have the targeted area for cdbg and then perhaps open up with this unique one time funding to the the i i agree with you like it shows more impact but then i worry that some of the businesses that need it the most like in ferro road and some of these areas that aren't necessarily entertainment districts yet but could be um they would miss out i should target it in that area so is the recommendation for parts like the arpa money into four parts are i was just saying open it up citywide and see what you get um and then if you need to allocate based on district if you have so many applications maybe you know that would be up to you all but that's my recommendation yeah and we can go into the different districts and kind of do a push for we go out and share information with the businesses to make sure they're aware and we have had times where we have gone to businesses because they look so bad yeah like because those are the ones they may not realize they needed um to your point there's a i think there's a market starting up in edgewood that i think could really use some of these facade grant fundings because they are going to offer some fresh food foods and everything okay okay is it edgewood or in that pocket this account lost from um deacon voters reds barbershop it's the new appointment in second azure no i'd like to see it prosper thank you for speaking up um i will say too because it's one time money i think that is an opportunity to do citywide you know something that we wouldn't normally do i'm i'm trying to look at it and all from all different angles um has the dollars to stow applied for this because i know brian he was interested in getting hasn't been able to apply because that wasn't in the targeted area but he would be eligible if we open it up okay yeah that would be he's working really hard he's a tenant of that property and that's fine we would just have to get approval from the property owner which i was going to say i think are his parents but that but that the other suites in that development could also apply yeah yeah now what we have talked about is um if we have a owner that owns multiple like in that one if he owns three we have another where there's a shopping center limiting it to maybe two just because if someone has you know a shopping center with ten store funds that could easily take all the money so we might do something where we say two um depending on funding availability so if we still have funds available you know in a year that maybe they could come back citywide so i think the consensus citywide is focused on the arpa money and that the block grant obviously has restrictions and guidelines and census tracts tied to it as well i'm assuming it does and so what 250 is already allocated towards five points it has been through your actual plan right through for this year but yeah it is almost time to apply for funding again so if there's we can definitely do some research to see if there's another targeted area for future cdp no i think yeah i think there's plenty of areas we can talk a little bit i would i would push my opinion would be or i would like us to consider moving the arpa money to to open it up to yeah that's what i there's just some really i think there can be it may not all happen in one area but i do think where it does happen will create a big impact i think so too sometimes just planting the seed right it does it does have a um a trickle down effect like it does you see the net the business next door starts making improvements and um so it does impact the entire area this was really helpful we needed to get that feedback thank you iisha thank you thank you and then you'll come back or send a recommendation on some definitions of language um i didn't do the best job on timing you all are just really working quickly today so we were planning for you all to have some a little bit of a break and some lunch um now at well 11 yeah so we can go ahead and do that if you like about 15 minutes too we're having a working lunch we can start up if the consult we can get the consultant um there's a consultant that has to be present for a second of session okay so we'll need them to be able to set up half here half virtual okay so just need time to get them in place right yeah ready i don't know do you want do you want us to go are we going and do you know yeah the lunch will be here at 11 so if you i don't know if y'all need to just do what you need to do we'll go ahead and go into executive session now and that will cover us through we can have lunch in the executive session and do the discussion right but i need time to get them set up they're not due to be here just quite yet so so what she's saying is we have about a 15 minute break you like us to do that now madame clark or would you like us to do that at 11 we do it now that way we can go ahead and set down the audio okay mr. mayor i mean we go into executive session for discussion of negotiations incident to propose contractual arrangements pursue it to seco 30 days 40 s 78 to crawford consulting thank you most is a second second uh any questions concerns hearing non-seeing i'm madame clark can you read the role please mr. brown yes yes you are not


We don't have a lot of time. You want to learn how to increase your chances of getting medical school. I made this video just for you. So let's get into it after this intro. All right guys, what is going on? Luxury from the empty journey, helping you succeed on your medical journey with less stress. Today's video is all about quick tips to help you increase your chances of getting into med school and becoming a doctor. So I'm gonna get right into it. We're gonna put three minutes on the clock. Let's see if I can get there. Tip number one is to make sure you submit your application early. I can't stress this enough. Most of you guys have probably heard this tip, but I want to make sure you understand why. Most applications for United States med schools goes around in April, early May. And Texas medical schools have a totally different application. Also opens up at the start of May. You want to try your best to submit your application the day it opens or within the first week. 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So it kind of goes back my last tip of think about your experiences, think about the takeaways and find some common core or cores that are just different or unique because you wanna be memorable during interview process and definitely during the application process. So just take some time, just invest some time to figure out what your angle is, what makes you unique because then once you figure what your angles are, you can then structure your application, your essays, your interviews all around it and be sure when you walk out of the room that person is gonna definitely remember who you are. And that guys is the tips to really increase your chances of going to medical school. I know the video was quick, but those are really powerful, non-fluffy tips that you can use to just immediately increase your chances of getting into medical school. Now, if you want more, obviously the video was quick, then I recommend you guys go on Amazon and check out my book called The Pre-Med Journey, which is basically a start to finish guide on how to increase your chances of getting into medical school from studying to all the way to applying. And it's only 99 cents on Kindle. Again, that will be linked down below if you guys want it. If you guys did enjoy this video and you want me to make more videos on pre-med topics or anything related to getting into medical school, make sure you comment down below and I'll be happy to take those suggestions in the future. If you did enjoy this video, make sure you give a like. If you're not subscribed, make sure you join the community. And if you are subscribed, thank you for your support. I highly appreciate it. And that's gonna be it for this video guys. If you guys have any questions, you know where to find me, I'll see you guys in the next one. Take care of my friends.


update. Okay, folks, I posted a Larry Pesaveto for TF&N. I posted the chart here of the E-mini S&P. We said this in the video before the market opened today. Look for an ABCD to potentially go short up there. And you can see at 5086, that was the ABCD. Now you're at a break-even point if you're in that particular thing. Now, folks, I have to bring something to your attention here. It was brought to my attention by our good friend down in Florida, Dr. E.S. and it was a quote by Dr. or President Ronald Reagan. I forget which speech it was, but he said there was a clergyman and a politician who were both passed away and they were on the way to go pearly gates. And when they got to the pearly gates, St. Peter came up and he said to the clergyman, here's your room, sir. He says it's a single room, one table, you know, one mode and one bed, and that's what you get. And the politician who was also passed away, they said, well, what do I get?  He said that this is incredible. He says, well, why is it that I get this and the clergyman who spent his life on the Lord gets that? He says, you don't understand how things work up here in heaven. He said, first of all, he said he's worked hard, yes, and he gets his reward up in here. But sir, we've never had a politician to make it this far. When I heard that last night, I laughed so hard, because several reasons. One of all, if you ever saw the movie Pretty Woman, that was Chasen's Restaurant in Beverly Hills. That's where I was hired by Drexel Burnham back in those days. That's why it has such a strong meaning for me. Anyway, that's when I watched that. And when I saw that joke, I bet Mr. Reagan and his wife several times over the years, because one of my very good friends was a major supporter of his, helped him get elected governor and also president. But anyway, that's neither here nor there. Here's what we're looking at.  And we're seeing what's going on. We're just one thing after another. The other one that we want to talk about is our good friend, Mike Moore, is going to be on the air here just a minute at the break. And we want to talk to him about his uncanny call that he's made in Crude All Today, folks. Really amazing. So stay with us. We'll be right back.<PHONE_NUMBER>.


The challenge of the Yukon It's Yukon King Swiftest and strongest lead dog of the Northwest Placing the trail for Sergeant Preston of the Northwest mounted police in his relentless pursuit of lawbreakers Gold gold discovered in the Yukon a stampede to the Klondike in the wild race for riches Back to the days of the gold rush with sergeant Preston and his wonder dog Yukon King as they meet the challenge of the Yukon When her grandfather died Norma Roswell came to the Yukon territory to take over the fur company which the old man had owned and operated The company was located in Dawson City Norma knew absolutely nothing about the fur business and She admitted as much to Hugo Groton her grandfather's assistant who had been managing the business since the old man's death Frankly, Mr. Groton. I feel pretty helpless trying to take over a business that I know nothing about I'll have to rely on you to run things while I'm learning my way around you can rely on me completely Miss Roswell In fact, you lead in trouble yourself about the details at all. I doubt if an attractive young lady like you would find it very interesting anyway You were my grandfather's bookkeeper, weren't you? That's right When his health began to fail last summer I more or less took over the active management of the company I really don't even know the simplest facts about the business Where do we get the first that we handle from trappers? Yes, we buy from trappers and also from traders who operate trading posts out in the wilderness and we ship the first to the states Is that it? That's right. There's an agent in San Francisco who markets the first for us I suppose the warehouse down by the river is where we store the first for shipment exactly exactly We receive the first here at the office and transfer them down to the warehouse at the end of each week I'm learning fast. There's a great deal to the fur business Such as learning how to judge the quality of furs and how to bargain with the trappers and traders But as I say you can leave the details in my hands I'll have to until I learn more about the business It's past two o'clock if you'll excuse me miss Ross Well, I'll drop over the post office and see if any mail has come in for us from our agent in San Francisco Do you think it's safe to leave me here in charge? Oh, yes, of course the clerk will be here to help you and if anyone should bring in a load of furs You can ask them to wait around till I get back. All right, mr. Groton. I can manage Instead of going to the post office Hugo Groton went to a cabin on the outskirts of town Inside the cabin a group of hard-looking men were playing cards The leader was a big black bearded man named Turk Malone. They looked up in their game as Groton entered Howdy Turk. Hello boys What's the deal are we still gonna be able to keep going with our deal now that the day was taken over the campaign Sure. I sure don't worry about her She's a babe in the woods doesn't know a thing about the fur business. So she'll have to leave everything in my hands Then you'll still be able to handle all the stolen furs. We bring you certainly the same arrangement as always I pay you gender generous price for all the furs you bring in and I enter that price on the company books Then afterwards you kick back half of the money to me. You sure don't cheat yourself, honey Do you we take all the risk you rake in half the profits? What are you complaining about? I'm providing you with an easy way to get rid of all the furs you steal. In fact, the whole scheme was my idea Now Not those furs that flat nose brought in this morning. I Paid him six thousand for the lot of them Which means I have three thousand coming back to me. They had to move over three grand flat Okay, Turk got it right here in my pocket. There you go Groton One thousand Three thousand thank you Well, I'd better be getting back to the office In the meantime Keep up the good work Meanwhile at the fur company office normal Ross. Well was receiving to visit it I'm Sergeant Preston Northwest Mounted Police. This is a friend of mine Hal Bradford. How do you do? I sure am pleased to meet you miss. Won't you sit down? Thank you What a beautiful dog you have Sergeant. What's his name King? He's the greatest dog in the North country I hope you don't mind my bringing him into your office. Oh, not at all sergeant. I'm very fond of dogs You're new to the territory aren't you miss Roswell? Oh very much. So I just arrived in Dawson yesterday You see my grandfather died several months ago and left the company to me So I came to the Yukon to take over you're going to operate the company or so I'm going to try for the time being though. I'll have to depend pretty heavily on Hugo Groton He's been taking charge of things since my grandfather's death. Yes, I'm acquainted with him What was it you wanted to see me about sergeant in the last few months has been an outbreak of fur robberies all over the territory Trappers have had their fur stolen two of them have been shot to death We're pretty sure the same gangs responsible for all of the crimes But up until today we hadn't been able to get a lead on them or trace any of the stolen furs And now you have a lead. It's not exactly a lead yet Eventually it may help us catch the criminals What exactly do you mean how Bradford here is a trapper? He has a cabin out on the Squaw River Several days ago his furs were stolen while he was out tending his trapline Oh, I'm sorry to hear that not have as sorry as I was luckily howl took the precaution of branding a small mark on each Pelt so now he'll be able to identify those furs if they ever turn up. Is that it? That's right Now be able to prove they were stolen from me But why are you telling me all this the gang must have some way of disposing of all the furs they steal I'm probably selling them the various fur company trading post you mean they may have sold some to this company quite possible As your company received any furs in the last couple of days Oh, yes, we received them this morning, and I know there've been others there in the back room waiting to be transferred to the warehouse Would you like to look them over? Well, you sure would all right? I'll show you where they are They're right in here What sort of furs were stolen from you well among them there were a couple of dozen silver foxes a lot of beavers and links And a couple of Wolverine pelt I believe that's just what was in the bale of furs. We received this morning They're right over here in the corner. Golly. Those look like my furs. See if your brand's on the pelt It's there all right. Take a look Small X mark. That's right. I'll bet it's on every pelt in this bundle. Let's see Sure, it's on the next one and this one this one too. I found it. There's no doubt about it These are the furs that were stolen from me who brought in this bale of furs miss Roswell Why I really don't know sergeant. I was here when it happened that mr. Groton handled the transaction What does the man look like? Well, he was heavy set and his nose was flat as though it had been broken He was wearing a wool cap and a Mackinac. Did Groton know him by name? I'm not sure. You see the man was already here when I arrived at the office this morning Oh, mr. Groton was examining the furs and then a little while later. He paid him off and the man left Oh, that's probably mr. Groton now. Maybe he can tell you more. We'll go out and talk to him Sergeant Preston too was anything wrong this bale of furs you bought this morning was stolen from Hal Bradford here Stolen you say that's right. I identified him by a mark I branded on the pelt I told sergeant Preston what the man looked like who brought them in perhaps you can tell him who the man was why? Well, no, I don't know who he was you had any dealings with him before. No, I'd never laid eyes on him before this morning This was well says that he has a flat nose And that he wore a Mackinac and wool cap. Can you add anything to that description? No, I don't believe I can To tell you the truth, I didn't pay much attention to his appearance Well, he shouldn't be too hard to identify Notify the city patrol maybe we can pick him up before he leaves town. All right, Hal. We may as well be going come along How How would you like to do me a favor? What shirt sergeant? What's up? I'm wondering if Hugo Groton may not know more than he's telling Groton What do you mean when he found out the truth identified the stolen furs and we have a description of the man who brought the men I got the impression that he was a bit frightened. Well, yeah, not to mention that he did seem kind of nervous. I Still don't see exactly what you're driving it Groton's been in complete charge of the Roswell fur company ever since the death of Miss Roswell's grandfather That means that he's been in position to dispose of all the furs the gang's stolen in the last few months I get it. I think he's working in coasts with a gang. It's just a hunch but it may be worth following up What is it you want me to do for you, Sergeant? I'd like you to wait here and keep a watch on the fur company office If Groton leaves the office follow him and let me know where he goes. Sure. I'll do it Well, what's the idea? Groton really is working with a gang. He'll be worried that we might find the man who stole your furs So probably try to warn him as soon as possible to stay undercover. Why sir, if I follow him I can find out where the gang's hideout is. That's right Now keep out of sight as much as possible so Groton won't see you and just follow him wherever he goes Don't try to investigate any further. Notify me at headquarters and let me handle the situation. Right 20 minutes later Hugo Groton emerged from the fur company office and went back to the cabin on the outskirts of town Where he had met Turk Malone and the gang of fur thieves He didn't know that how Bradford was following Where's flat nose? He went out a while ago to get some tobacco Well, what's wrong? Plenty Those furs he brought in this morning have been identified by the trapper. He stole them from identified Okay, it seems the trapper put a brand mark on each pelt and that's not all the Mounties have a description of flat nose And they're out looking for him right now You've got to keep them out of sight until the search dies down.  I'll say I know him flat nose He's the trapper whose furs you brought in this morning. Yeah, what's that? Well, I was coming back to cab and I spotted this guy trailing groton after Groton went inside He hung around for a minute or so Sort of sizing up the place So I figured that but put a gun on him find out what he was after.  We'll see to that Wait a minute Turk If you're thinking of killing Bradford that may not settle things What do you mean or all we know it was the Mounties who told Bradford to keep a watch on me If so, they're going to get mighty suspicious when they find out he's disappeared Never thought of that you ain't suggesting we ought to turn him loose. I am not by a long shot What do you think we ought to do groton? I have a scheme that will account for Bradford's disappearance and at the same time put me completely in the clear It'll make the Mounties think I had nothing to do with the fur robberies. Let's hear your scheme Now here's what I've got in mind Right after I go back to the office flat nose can show up again with another bail of furs Hey, I don't like to hold your horses a minute and listen As soon as you show up I'll pull a gun on you and pretend I'm going to holler for the police Well, then what then you jump me and take the gun away from me There'll be three of us there at the office me and normal Ross will in the clerk You can tie us up or lock us in the back room and make your getaway and let her put you in the clear all right But how will that explain Bradford's disappearance? Very simple The Mounties will think Bradford spotted flat nose and went after him. They'll wait for him to come back And when he doesn't show up, they'll figure he ran into trouble Yeah, I said that's pretty smart Later that afternoon after Hugo Groton had returned to the fur company The crook called flat nose entered the office the clerk stared at him in surprise Well, what do you stare at me that way for why why no particular reason I'm just surprised to see you come back You were here this morning. Weren't you? Well, what if I was? It happens. I got another bunch of furs to sell Where's the factor mr. Groton's in his office talking to miss Ross? Well the owner of the company. I'll go get him You wait right here. All right make it snappy certainly. I'll get him right away Mr. Groton, yes, what is it dad that man who was here this morning the one sergeant Preston is looking for he's here again What's that you mean the man who sold us those stolen furs? That's right, mr. Ross Well the fella with the flat nose.  We'd better not take any chances I have a gun here in this drawer Here it is. What are you going to do? I'm going to cover him with this gun and make sure he doesn't get away For heaven's sakes mr. Groton be careful if he's a member of that gang he may be a killer.  Well, I can handle him Get your hands up mr. Hey What are you pointing that gun at me?  All right. All right, but what's the idea? The game's up mr.  Oh, yes, we can the trapper has already identified them by a mark. He branded on each pelt Now then I'd better search you and make sure you're not carrying a gun. Oh, no you don't That's better now reach all of you What are you going to do? I could kill a whole bunch of you But the shots are make too much noise, so I guess I better just lock you up in the back room Alright get moving a A short time later at mounted police headquarters sergeant Preston was talking to Constable Alex Ross Any report yet from the city patrol Alex? Not yet sergeant, but they've all been notified to be on the lookout What's the clerk from the first company? What's wrong? That flat north fella. He just showed up again at the office. Oh still there Oh, he got away mr. Groton tried to hold him with a gun But he knocked Groton down and got the gun away from him. He locked us all up in the back room Well, you just broke out a few minutes ago. Come on Alex. We'd better get over there When the two Maldives arrived at the fur company office they learned the details of what it happened No, my Ross. Well had been much impressed by Hugo Groton's apparent bravery even though that cook got away I think it was very brave of mr. Groton to do what he did. Don't you sergeant? Yes Are you sure you feel all right mr. Groton your jaws swollen? Yes. Yes. I'm quite all right. Thank you He hit me pretty hard, but I feel all right now strange He should have come back again the same day you say what he wanted He had another bunch of furs with him that he wanted to sell us probably stolen like the first bunch probably so Any chance of King trailing him sergeant? I'm afraid not Alex He'd left something behind or if the office were empty it'd be a different story But as it is there's no way for King to pick out his scent. Isn't there any hope of catching him? Oh, of course there is mr. Roswell, and I'm sure we shall send her later Oh, by the way, were you living in case I have to get in touch with him at the Victoria Hotel? I guess you know where my cabin is located. Yes, I do. All right, Alex We might as well go back to headquarters right now. I think more we can do here I guess this puts Groton in the clearing side of looks that way Alex apparently my suspicions were wrong Where's Hal Bradford? Why I posted him right here in the shadow of this building. It's not there now Where do you suppose he's gone? He must have seen the flight nose man decide to trail him to the gang's hideout Oh, yeah, that must be it.  Let's hope so Alex Nightfall came there is still no word from Hal Bradford By seven o'clock the sergeant began to be seriously worried in spite of constable Ross's efforts to reassure him Lux sergeant. There's no call to be worried The crook headed out to the creek somewhere. It may be a couple of hours yet before Bradford gets back to town Maybe so Alex, but I still can't help worrying Anything's happened to Hal. I'll feel responsible. I'm sure he's all right. Hey Wait a minute. What's the matter? I'm wondering if we were right to eliminate Groton as a suspect Well, sure. Why not? If he were mixed up with a gang he would have worn the flat nose man not show up again And when he did show up Groton certainly wouldn't have tried to capture him There'd be too much danger of the crook squealing on it. True enough But suppose that whole incident was staged just to make it look as though Groton were innocent You mean the flat nose man showed up again just so Groton could put on an act for our benefit? That's right No, but lucky if they cooked up the whole thing beforehand just to throw us off the scent That means Groton must have gone to the hideout and told him about the furs being identified That's just the point for all we know Groton did go to the hideout We've been figuring that how followed the flat nose man, but he may have followed Groton and been captured by the gang Holy smoke. I never thought Alex. I'm not going to wait any longer I'm going to talk to miss Roswell and find out if Groton left the office any time after Hal and I were there I'll go with you sergeant. All right. Got your park. I must go a Short time later the two Mounties arrived at the Victoria Hotel knocked on the door of normal Rosswell's room.  We just stopped by to ask you a question Do you know Hugo Groton left the office between the time how Bradford and I was there and the time I came back with Constable Ross Why yes, he did he went out just a little while after you and mr. Bradford left with the stolen furs Why you say where he was going? Yes, he said he was going to the Yukon Territorial Bank to discuss our account with the manager. Thanks. That's all I wanted to know Why do you ask sergeant is anything wrong? Why hold not miss Roswell? I'm just checking out that song. Come on Alex After leaving the hotel the two Mounties went to the home of the bank manager Henry McLeod What was it you wanted to see me about sergeant?  Why of course he's the manager of the Rosswell fur company the Groton come to see you at the bank this afternoon No, in fact, I haven't seen him for several weeks. Were you at the bank all afternoon? I Come back immediately after lunch and dinner leave until five o'clock then there's no chance that Groton came to the bank And mr. Of course not sergeant. I'm sure he never came in thanks for the information Alex I think we'd better go to Groton's cabin have a little talk with him Meanwhile after locking up the office for the night and eating his evening meal at the cafe Hugo Groton had gone to the gang's hideout Howdy boys By time he was showing up good. What's the matter? You weren't worried were you well? We haven't you and our fingernails if that's what you mean But we want to find out how things stand yeah Well, you can relax everything's under control you mean they fell for that act you and me put on over at the fur company office We hook line and sinker. I could tell from the faces. They were plenty puzzled, but they're convinced I'm innocent What about Bradford they say anything about him not a word They're evidently assuming he followed flat nose just as I figured they would in that case We may as well get rid of Bradford right now sooner the better by thunder if you kill me You won't get away with it sergeant person. I'll catch up with you and you'll all swing for murder You'd better not kill him here. The shot might be heard. Don't worry. I ain't that foolish Me and the boys were figuring on heading down to the Pelly River country tonight We'll take Bradford with us and get rid of them somewhere along the way good enough Well, I may as well be getting back to my cabin. Yeah, no reason for us to squat here any longer either All right boys get your gear together hitting the trail right now When sergeant Preston and Constable Ross arrived at Hugo Groton's cabin, they saw that the windows were dark Looks like he's not home. I may have gone to the gang's hideout. Wait a minute. Here he comes now Yes, we were According to miss Roswell, you left the office this afternoon shortly after Hal Bradford identified those stolen furs Yes, that's right. I did mine telling me where you went. Of course not. I went to the Yukon Territorial Bank I wanted to see the manager about the company account. You're lying Groton See here sergeant I don't like your breath Groton I've already talked to the manager and he says you never set foot in the bank this afternoon. I Why are you checking up on me this way? Hal Bradford was told to follow you whenever you left the office He hasn't come back. What happened to him Groton? I don't know anything about Hal Bradford Oh, yes, you do. There's no doubt you're mixed up with that gang of fur thieves I'm warning you Groton. You want to save your own skin. You'd better tell the truth.  Where were you coming from just now? I I was out for a stroll. That's out for a stroll, huh? Maybe a spell in jail will refresh his memory. Yes, sergeant. There's no time for that Alex How may be in danger right now? What are you going to do first? I'm going to search Groton now Wait a minute Preston you can't play it and stand still Oh Carrying a gun, eh? I'll take charge of this for the time being. Now what Sergeant? We'll have King follow Groton's back trail It just came from the gang's hideout. King will lead us there. Hey boy Get this man sent King All right backtrack King backtrack King had been trained to understand such a command with an eager bark He pounded forward get moving Groton. You're coming with us King led the sergeant to the cabin on the outskirts of town, which the gang had just vacated So you were just out for a stroll they go I'll strike a match sergeant There's a candle on the table there. Good. I'll light it Place is empty. Yes Look for these cans and bottles people have been living here very recently King had caught a familiar scent the scent of the man Who had been with his master earlier that day? Suddenly he gave an eager wine. What is it boy? It's hard something It's a mitten Alex. This is one of Hal Bradford's mittens. Are you sure? I'm positive He made them himself out of Wolverine fur We're showing them to me this this morning the gang must have been holding him prisoner here. All right, Groton Things just prove that howl did follow you here to this cabin. You're still going to play innocent I have nothing to say. I've already told you I know nothing about Bradford very well search yourself But I warn you if anything has happened to howl you'll hang for murder Take him to headquarters and hold him on suspicion and we're coming back to this cabin and put King on Bradford's scent Meanwhile Turk Malone and the other four members of the gang were traveling southward Several hours after leaving the cabin. They came in sight of a small canyon Howl Bradford was lying on Turk sled bound and gang That can you know where there's a good place to get rid of this guy We'll take him down there shoot him and dump his body Be spring before anyone finds him. You ever do find him that easy. Let's go A short time later the gang halted their teams inside the canyon. Oh, you much Where you get off even me to that snow grip turn that's what I'm gonna do I Which one of us is gonna plug him that don't matter You know take a few pot shots at him with for target practice I'll take the first shot Here goes as Turk raised his gun to fire a shot suddenly rang out from the rim of the canyon Turk fell his flat nose raised a cry of alarm Mounies up there in the cliff The crooks dropped to the ground behind their slaves and tried to shoot it out But the Mounties had the advantage of a higher position And after two more the gang had been put out of action the remaining two men quickly gave up the fight Well Constable Ross remained on the cliff keeping the men covered with this carbine Sergeant Preston descended into the canyon and took charge of the situation After he had collected the crooks guns Constable Ross followed him into the canyon and helped him handcuff the prisoners Then the sergeant untied Hal Bradford. There you go. How? He was sure saved my life sergeant man alive. I thought I was a goner. Sorry.  I was hoping you'd find that mitten You're drafted on purpose. Yeah, just in case you did locate the hideout I managed to pull it loose just before the gang hauled me out to the sled I figured I'd recognize it because I was showing you my mittens this morning. It's a good thing you did Where's Groton up they took him to hand quarters and how him on suspicion in spite of the evidence He refused to admit that he was mixed up with a gang or do anything at all about your disappearance Groton thinks he's gonna leave us all in the bag He's got another thing coming He was the one who steamed up all these fur robberies the first place Yeah, you're doing right. He was and I'll testify to that in court Don't worry with your testimony and that of how Bradford will have no trouble convicting him three of the gang Wounded to wearing handcuffs and Groton and custody back at headquarters Looks like we'll have no more trouble with this particular gang of fur thieves a sergeant right Alex Once Groton and these men have been sentenced this case will be closed On a lonely trail near Selkirk Dave that money sergeant Preston is in town. We can't take any chances with him so close.  Well, he'll be found with a bullet in him. So stop worry Remember Logan's luck still holds Yes, Sergeant Preston and King have come to Selkirk trail the Logan gang And it might be that Dave Logan may find the chance to put a bullet into Preston when things come to a show Down be sure to listen to this next exciting adventure Logan's luck These radio dramas a feature of the challenge of the Yukon Incorporated are created by George W. Trendall produced by Trendall Campbell Enterprises supervised by Charles D. Livingston and edited by Fran striker the part of sergeant Preston is played by Paul Sutton They are brought to you once each week Until September when we shall resume our regular Monday Wednesday and Friday broadcast This is Jay Michael wishing you goodbye and good luck until our next broadcast


Alright, so we know that the expression is not constant in simple harmonic motion, right? So we cannot use those equations of motion that we have learned in the kinematics because those equations of motion v is equal to u plus a t, s equal to u 2 plus half a t square and the third one, all of them were derived by assuming expression is a constant, right? So we can never use those equations in the case of any oscillation, okay? And we are learning a special kind of oscillation, which is simple harmonic motion, right? So we'll start the class with a couple of examples on what we did last class. And before I do that, before I take up the examples, we'll list down the equations of motion. So if you type in what are the equations of motions you have, all of you, what, which equation of motion you remember, type in, okay, Rubau, we cannot use that. That equation is valid only for the constant acceleration, alright, okay? So the first equation is this, a is equal to minus of omega square x, alright? Then the next one, what else? Anything else? Mudit, this is your first class, first session you were joining, Mudit? Yes, sir. So you are aware of simple harmonic motion? Anything? No, sir. No? So you are joining in the middle of a chapter, okay? Yes, sir. So it may be half an hour, 15 minutes to get in the groove, right? Now, since you are in middle, it might be a little difficult, but then you can make an effort. It will be not so difficult also. Yes. Alright, so, fine. So we have another one, Siddhas is mentioning this, v is equal to omega root over a square minus x square, right? So first equation, first equation of motion is between acceleration and x. What is x, everyone? What is x? Displacement, no. What is x? Anyone? It is the distance from mean position, okay? It is a distance from mean position. And when you measure the distance, one side can be positive and other side will be negative. You can do that. Displacement, you know, requires two points. You have to say from where. So this is from the mean position. So v is equal to omega root over a square minus x square. And by the way, do you know what is the name of omega? Omega is what? Write down, omega is angular frequency. Now any other equation, other than these two, okay, Aditi has written 1x is equal to A sin omega t plus phi. Now tell me what is A, what is it? Capital A is amplitude, correct? And how you measure it physically, what it is? How will you identify the amplitude when an oscillation is going on? Physically what it is? Maximum distance from the mean position, okay? Maximum distance from the mean position. What is the condition for a mean position? How you know where is the mean position? Condition for it is what? Acceleration is 0, right? You can see A is equal to omega square x. At mean position, x is 0. So at mean position, at mean position, acceleration is 0. So force will be what? Force is also 0, okay? In which direction along the SHM direction, right? So we have seen all of this last class, I am quickly summarizing. Any other equation? First one is between acceleration and displacement. Second one is between velocity and displacement. What is x versus t? Next, you can differentiate x to get velocity. So v is equal to omega A cos of omega t plus phi, okay? And you can differentiate it again, you will get A is equal to minus omega square A sine of omega t plus phi. So how many equations of motions are there? One, two, three, four, five. You already have five equations of motion for SHM. Do not use those three, all right? So let's take a few questions on these equations. How we can use these equations to analyze the simple harmonic motion. And by the way, what is phi before I proceed with a question, phi is what? Phi is what? We have derived it last class, tan inverse x by A. Do you remember this? Do you remember it? Look at your notes, all right, fine. So first of all, if equation of motion is this. x equals to A sine omega t plus phi. You need to tell me what is the time period of the oscillation, time period of oscillation is how much, how will you calculate it? Find out, wait, sorry, it was sine inverse, it is corrected, it was sine inverse, okay? That is what we derived last class. Time period of oscillation, all of you find out, yeah, yeah, sine inverse. Anyone close, no one, okay, all of you. So if capital T is the time of oscillation or time period, okay, then whatever was happening, and it means whatever was happening at T equals to T, same will happen at T equals to T plus capital T. Yes or no? Oscillation should repeat after every fixed interval time, and that is what the time period is. So we need to find out what is this capital T. All of you agree to this? Everyone type in, right? So if X is equal to A sine of omega t plus phi, after T plus capital T, it should be the same. This should be equal, also equal to omega t plus capital T plus phi, both should be equal because after capital T it will come back to the same thing. This is equal to A sine omega t plus phi plus omega capital T. This should be equal to A sine omega t plus phi. So what should be the value of omega capital T? So that both are equal. One value is omega into capital T should be equal to zero. What is the other value for which these two are equal? So what should be the value of omega into capital T should be equal to, everyone, you know, right, how is the sine curve? Sine curve is this. This is the sine curve, right? This is the sine curve, all right? So you are, let's say you're talking about displacement X. This is X and this is T, all right? So same thing will happen at this point and then at that point, okay? Now you will say that, no, no, there is a point, you know, there is this point, same thing is happening here also, okay? You can say that it is not 2 pi, but then you will take this point, then you have to go away a distance of 2 pi only. This distance you have to take, okay? If this is the angle, okay? This is your angle you are plotting. Then after every 2 pi angle, sine function will repeat itself, okay? This is zero, this is pi, this is 2 pi, this is 3 pi, okay? So when omega T becomes 2 pi, same thing will repeat for every point. I don't, I'm not concerned with only one of the points. All the points, whatever is the value of small t and phi, same thing should happen and that will happen when omega T is equal to 2 pi. So time period of the oscillation is 2 pi by omega. This is a time period and from here, frequency of oscillation, which is 1 by time period is omega by 2 pi. All of you understand this? If you understand, right? So if you know what is omega, you can find out the time period, 2 pi by omega and omega by 2 pi is the frequency, okay? Now, take few more questions. So like I told you last class, this chapter is divided into two parts. One part deals with the kinematics of simple harmonic motion. Other part deals with the laws of simple harmonic motion. So right now we are focusing on the kinematics part of it, okay? So let's say this is the mean position, okay? Amplitude is A, fine? So at mean position, let's say velocity is U. Velocity is U. You need to find out the distance from the mean position, how much it will be for point which has the velocity equals to half of the mean positions velocity. All of you do it. These are very direct type of questions. Little bit of carefulness if you show, you will get the answer. Equations of motions I have already written. No one? Which equation of motion will you use here? Which one will you use here? All of you tell me. These are the equations of motion. Which one will you use? I am asking you that where is the location at which the velocity becomes half of the mean position? At which the velocity becomes half of whatever is its velocity at the mean position? Which equation will you use? Tell me. Second one, there is no doubt about it, right? Second one only, isn't it? This one will use, alright? So let me write that equation since you have identified it. P should be equal to omega root over a square minus x square. Can you tell me what is the velocity at the mean position with respect to this formula? Using this formula, can you tell me at mean position what will be the velocity? Everyone, at mean position, correct, at mean position x equal to 0. So v is equal to omega a, v is equal to omega a. So we need to find out a point which has velocity, how much? Which has a velocity of omega a by 2, okay? Half of the mean position velocity. So just substitute v as omega a by 2 and you will get the answer. Can you tell me quickly what is the answer? Omega is gone. You could have watched the video, recorded video of the previous class. So after the class, ping, push power me, I'll forward you the previous class recording, okay? Okay. So x square is equal to 3a square by 4. So x is root 3 by 2 times a. Is this the correct answer? I mean, can there be more than one point? Everyone? Is this the only point possible? Can I say plus minus? Other direction also? No. If you talk about at this point, there will be one velocity going this way and other velocity going that way. At every point, you have both the directions of velocity while going away and while coming back, okay? But the point is there will be two such points. x equal to root 3a by 2 and x equal to minus root 3a by 2. Because the SHM is symmetrical about the mean position. Whatever that whatever happens on the one side of SHM, same thing happened on the other side of the SHM also, okay? Okay. So I hope it was a straightforward thing. So this one, you don't have to solve anything. Just describe the motion a, b, c, d, these are the forces acting on a mass. So can you tell me what happens if this kind of force acts on a mass? Anyone? You don't have to find anything. When this kind of force 3x plus 3, will it do SHM? Will it do SHM? If I apply that kind of force, what will happen? This force if I apply, let us visualize, you know, there is a mass like this, okay? It is kept at let's say x equal to 0. At x equal to 0, what is the force acting on this block? How much is the force? 3 Newton? 3 Newton, so 3 Newton is acting on it. What will happen to this block? This blocks, this block will move forward, right? This block moves forward because of the force. Now after x will become, let's say here x was 0. After it moves forward, x will become equal to 1. So now what is the force? What is the force now? 6 Newton? So do you guys see that as it is getting displaced on the right hand side, the force is getting increased more and more, right? So will it perform SHM? Will it ever come back? Will it ever come back? No, right? So no SHM, okay? For A. Now similarly, I want you to analyze B also. Everyone, do it. Is B SHM B? Is this SHM equation? Will it do SHM? No. At x equal to 0, what is the force? What is the force at x equal to 0? Minus 3. So the force will act on this side. Force acts on this side, okay? Then x becomes, let's say minus 1. What is the force now? When x equal to minus 1. Now what is the force? 0. 0, right? Right now it is 3 Newton this way. Now the force is 0. And then it further displaces to x equal to minus 2. Because acceleration is 0, velocity is not 0. Velocity is not 0, acceleration is 0. So let's say you go to x equal to minus 2. What is the force now? At x equal to minus 2, 3 Newton. So you'll get a force. Force will change its direction or not? Force will change its direction. Earlier it was minus 3, now it is plus 3. So 3 Newton on the other side. So you can see that it is, when it is going from here to there, it was decelerating, okay? So now the object will come back, alright? And when it goes this way, x will become positive. Force will become negative. So it will get pushed this way. When it goes this way, it get pushed that way. And when it goes that way, it get pushed this way. So every time it is getting pushed towards the mean position. And that is why here some sort of oscillation is going on. All of you are able to understand this. Everyone is able to understand, okay? So can you tell me where is the mean position? What is the value of x where the mean position is? Mean position is what? x is equal to what? x is equal to 0, that is the mean position, okay? So minus 3x minus 3, this is the force. x is equal to 0, so force will also be 0. So at x equal to minus 1 meters. This is the mean position, alright? This x and the x in the equation of motion, they are different, alright? This is x coordinate. Remember that this is x coordinate. And that x which you have in this equation, that x is a distance from the mean position. At x equal to minus 1, this value of x is 0. I hope you are able to understand this. They both are x only, but this is the distance from mean position, this is the coordinate, alright? So there is a simple way also to identify whether it is an SHM or not, you have to just see whether the force x coordinate, they are of opposite sign, okay? So if f is equal to minus cx plus k, where c and k are constant, then it will always be an SHM, okay? If f is minus cx plus k. So we have discussed it last class, right? That if expression is of opposite sign of x, it will be an SHM. If expression is opposite sign of x, the force is also opposite sign of x because force is mass and expression, okay? So now can you tell me is c SHM or not? You don't need to analyze it now. Is c SHM, everyone? If it is SHM, what is the mean position? It is an SHM because coefficient of x is negative and coefficient of force is positive, opposite sign. SHM mean position at x equal to 1, where 3x plus 3 is 0. What about d? Is d SHM? No, d is not a SHM, okay? Do this, do this. What happened? Where are you guys going? Area and punch, where are you going? All of you do this. Equation of SHM is this. X is equal to a sin omega t plus phi. Basically, I want you to find out what is the value of phi for this? Phi is how much? It is at a by 2. When t is equal to 0, it is at a by 2. Everyone, what is phi? If you are getting phi by 6 or 30 degrees, that is not correct. See, you need to understand one thing that phi is equal to 0 when? When it starts from here and go towards it, right? Phi is 0, right? When it reaches here, what is the value of phi when it is at a? Sin inverse x by a is what? When you go to a, at a, what is a phase? At a, what is sin inverse x by a? Phi by 2 at x equal to a, alright? So, this position is how? This position is that particle goes to a and then it is trying to come back. So, it has to be greater than pi by 2, right? So, if I tell you that particle is going like this, then your answer is correct. But it has gone like this and it is returning back. Are you getting it? So, it is not pi by 6. So, now tell me what it is. Don't treat it like a mathematics, okay? It is physics also. Do you all understand why it is not pi by 6? Everyone understood why it is not pi by 6? Okay, so tell me what it is? Phi belongs to, please remember, 0 to 2 pi. Phi cannot be anything but this. I don't know whether, I mean, you guys should come with whatever we have done last class. It is sad that you guys don't even look at what we have done, okay? We have discussed all of this. 0 to 2 pi, the angle will change. All right, so it has to be greater than pi by 2, all right? This is 0 angle. This is pi by 2 angle, okay? And then at this location, we need to find out what is the value of the phase 5. So, let us do one thing. At t equal to 0, x is equal to what? x equal to a, see this equation should be valid no matter what. So, a by 2, x is a by 2, this is equal to a sin of phi, okay? So, sin of phi is equal to half. So, according to this, the value of phi should be equal to what? Pi by 6? Can it have any other value? Can it have any other value? Can it be pi minus pi by 6 also? Can it? Do you guys know that sin of 30 and sin of 150, both are equal? Do you guys know this? So, when I say sin of phi is half, there are multiple angles for which sin of phi is equal to half. There are multiple angles, right? And if you talk about angles only between 0 and 2 pi, there are two angles. One is pi by 6, other is 5 pi by 6, okay? All of you understand this? So, one of them is correct answer here. How will you find out which one is correct? The answer to that is we need to write velocity also, differentiate x, you will get v is equal to a omega cos of omega t plus phi, okay? Now, put t equal to 0, v is equal to a omega cos of phi. This velocity, this is the velocity at t equal to 0. The velocity should be positive or negative. v should be greater than 0 or less than 0, everyone. All of you, this v should be less than 0 or greater than 0 in this scenario, in this scenario at t equal to 0. Less than 0. So, I have two values. You need to substitute these values and check which one will give you negative value of velocity. So, it is obviously that 5 pi by 6, when you put here, we will become negative. So, if you just look at x, there will be two values of angle while going and while coming back. But you have to look at the velocity also and its direction to find out which one of these two is the correct answer. So, phi is equal to 5 pi by 6, okay? This is the way mathematically you solve it, all right? Physically, you can solve it a lot easier. How? Can you tell me this red line, this one starting from here and this coming back? What is the total angle? Going to the amplitude and then coming back to the main position. Total angle is how much? Pi, 180 degree, 180 degree, right? From here to here, what is the angle? This angle, 30. So, subtract 30 from 180 because it is going towards the main position, all right? So, your equation of SHM is A sin of omega t plus 5 pi by 6, okay? Fine, let's proceed. If we are doing simple questions only, very simple questions these are, just that you are doing it for the first time, that's the reason why you may find it difficult to do this. Amplitude is how much? What it is? It is obviously 5 meters, 5 is the amplitude, okay? Time period, how do you find time period? You just did 2 pi by omega, omega is what? What is omega in this equation? X equal to A sin omega t plus pi is the equation of SHM, right? You compare it with equation of SHM, coefficient of the time t is omega, which is pi. So, t is 2 seconds, maximum speed is what? Vmax, how to get the maximum velocity? Maximum velocity happens where in SHM, at which location? Main position. At main position, what is the velocity? Omega A, what is omega? Pi, what is A? Phi, what is the answer for maximum velocity? Vmax is omega into A, what it is? 5 is A and pi is omega, 5 pi meter per second, okay? Now, do the next part. Velocity at t equal to 1. How you do this? Next part. Velocity at t is equal to 1, yes. Do it. How Anusha, how it is like that? Using fourth equation. For velocity, do not memorize things. It will, there is x and we know derivative of x is velocity, right? Derivative of x is V is equal to 5 pi cos of pi t plus pi by 3. Now, put t equal to 1 in this. So, 5 pi cos of t is 1, so pi plus pi by 3. How much it is? Cos of pi plus pi by 3, isn't it minus of cos pi by 3? Everyone, this is equal to minus of 5 pi by 2 meter per second.  Everyone understood? Type in. Is there any other way you can get the velocity? Any other way you could have get the velocity? Tell me. How else you can get the velocity? How do you get V from x? Differentiate dx by dt. V is dx by dt. Okay. Yes, another way is find x at t equal to 1. Then use V is equal to omega under root a square minus x square. You will get the same answer. If you are getting a different answer, there is a silly error somewhere. Do this. Anyone got equation of SHM? Find the value of pi. Will pi be less than pi or more than pi? What do you think? More than pi, right? If it starts from here, goes there pi by 2, then comes back, becomes pi and then it has travelled further this side. So pi plus whatever extra it has travelled this much. Okay. Or I got something. Others? Pi is equal to sine inverse x by a. So sine inverse of minus of root 3 by 2. So how much it is? Minus root 3 by 2. What is the value? Pi plus pi by 3. 4 pi by 3, right? All of you understood? Type in, is it clear? So 5 is 4 pi by 3. So we have got equation of SHM. So this is your first part. Second part. Do this. Assume time period is capital T. In terms of capital T, you have to find out. Let's say it is given. How will you proceed? What you will do? From its root 3 by 2 position, it has to go to the left extreme. From here, it has to go there. Take x equal to minus a. Very good. X is equal to minus a. This is equal to a sine of omega t plus 4 pi by 3. So from here, sine of omega t plus 4 pi by 3. So from here, sine of omega t plus 4 pi by 3 is equal to minus 1. What will I write? Omega t plus 4 pi by 3 as then, what is the angle at this point? When it reach here, sine inverse of minus 1 is 3 pi by 2. Omega t plus 4 pi by 3 is equal to 3 pi by 2. So what will be t equals to from here? Omega t is equal to x6 common 9 minus 8. So it will become pi by 6. t is equal to pi by 6 omega. Omega is equal to 2 pi by 2 pi by omega. Sorry, 2 pi by t is omega. So when you substitute that, you will get t by 12. This much time it will take. Can you go through it and let me know? Is it clear? Everyone? Is it clear? Clear? Parvati, is it clear? Gurman, is it clear? Yes, sir. Okay. After the class, you get in touch. We'll send you some recordings. Alright, do the C part. Find the time taken by the particle to reach the main position. What do you put X as when it reaches the main position? Just like you did the B part, same way. You have to do the C part also. The value of X will be what? 0. Of course it is 0. So 0 is equal to A sin omega t plus 4 pi by 3. Now my question is this will give you sin of omega t plus 4 pi by 3 is equal to 0. So omega t plus 4 by 3, 4 pi by 3 will be equal to what? What is the angle at 0 when it comes back after one round? Okay. So from here, when it comes back pi, then it takes another round from there and then comes back. So the angles, sin is equal to 0 when you do. You have to take it as 2 pi.  In fact, you get multiple values of sin for which this is 0. So this is 0 for 2 and pi. Okay. But then since first time it is coming back, we are doing it equal to 2 pi. Alright. So you'll get t is equal to 2 pi minus 4 pi by 3 divided by omega. This is how you do it. Right? So I hope you're getting idea about how to use the kinematics equations for the SHM. Alright. What is the doubt? Quickly type in, directly type in your doubt. Don't tell me that, don't make statements. Type your doubts. How it is 2 pi. Sin of 0 is what? Tell me. Sin of some angle is 0. So that angle should be equal to what? It can be 0. It can be pi. It can be 2 pi. It can be 3 pi. It can be 4 pi. It can be many angles. Okay. So 0 we have rejected. If you keep pi, you'll get t is negative because 4 pi by 3 is more than pi. So next value you have to put 2 pi. Time cannot be negative. It is time taken. Okay. Maybe 1 or 2 more questions. Just one more question. Then we will start something new. Answer for A part is what? Answer for part A. Yes. What is the reason? Force and coefficient of X. They are in opposite sign. Force is positive coefficient. X has a negative. So see it. Next. B. Anyone got the answer for B? Gourman got it. Aditi, Anusha. Equilibrium position. You know the name itself suggests it is equilibrium. So net force should be 0. Right. So when you put this 0, you will get the value of X to be equal to 4. So X equal to 4 is the equilibrium position. Fine. C part. Before you answer the C part, I want you to tell me what is the amplitude for this? Draw a diagram. You are solving a physics question. Don't do it without a diagram. Main position is X equal to 4. Where is the extreme position? Can you identify? Can you tell me where is the extreme position? Extreme position. Now read the question carefully. It is released at rest from X equal to 6. So suppose it is here at X equal to 6 meters. Which direction the force is acting on it? Everyone tell me which direction it is? Left or right? Force is negative or positive? At X equal to 6 meters, force is negative or positive? Negative. The force is acting this way. So there is a point where the object is at rest and it has started moving towards the main position. So can I say that this is an extreme position? Can I say that? Extreme position is X equal to 6. All of you agree? What is the definition of extreme position? Particle should be at rest and then after its velocity becomes zero, it should move towards the mean position. Are you getting it?  X equal to 6 is the mean position. Sorry, extreme position X equal to 6. So now tell me what is the amplitude here? Amplitude is how much? Correct. Amplitude is 2 meters. Now proceed with the C part. Write the equation of the motion. The equation of motion is X equal to A sin omega t plus phi. You need to tell me three things in this equation. A, omega and phi. X equal to 6 is an extreme position because it is at rest and it has started moving towards the mean position. That is what happens in the extreme position, isn't it? Extreme position particle is at rest and it starts moving towards the mean position. That is what it is. A, you have already found out two. Can you tell me phi? What is phi? It starts from the mean position on the right hand side. So phi is equal to what? What is the angle there? What is the angle on the right extreme? Over here. Angle is zero here. Over here, what is the angle? Phi by 2. So phi is phi by 2. A is 2. What is omega? How will you get omega? Tell me. Sine of omega t plus phi by 2 is equal to cos of omega t. I am asking you what is omega? Anybody got the answer for omega? Only shortage. Force A is 8 minus 2x. According to Newton's second law, this is equal to mass times acceleration. So acceleration is equal to minus 2 by m times x plus 8 by m. M is what? M is 2. So A is equal to minus of x plus 4. Now looking at this, can you tell me what is the value of omega? Your mean position is at x equal to 4. So you can write this as A is equal to minus of x minus 4. So your x minus 4 is your distance from the mean position. Let's say capital X. Now you can compare it with equation of SHM. A is equal to minus omega square x. So from here, omega is equal to 1. So omega is 1. So you have phi, A and omega. Clear to everyone? Type it out. See this x is different from this x which is in the equation. In the equation, the x is distance from the mean position. Distance from the mean position is x minus 4 because mean position itself is at x equal to 4. Mean position is not at x equal to 0. All of you type in, is it clear? Then we are done with this kinematics of SHM. So we are done with the kinematics of SHM. Now let us move towards the larger portion of the chapter.