Back in 2007, Nike flew me out to Los Angeles to work the first-ever Kobe Bryant Skills Academy. Nike brought in the top high school and college players from around the country for an intense three-day minicamp with the best player in the world, and for those of you that don't follow basketball, let me paint the picture. In 2007, Kobe was the best player in the game. Michael Jordan, who everybody's heard of, had already retired, actually twice at that point, and LeBron James as great as he was, he was still climbing that mountain. Kobe was that dude. Now, an important fact about me, as you've probably gathered from the pictures, I've spent most of my life in a basketball bubble. So I had heard the urban legend of how insanely intense Kobe's individual and private workouts were. And I figured, now I'm on camp staff. This is my chance. This is my shot. So my earliest opportunity, I walked up to him and asked if I could watch one of his private workouts. And he was incredibly gracious, and he smiled and said, sure, I'm going tomorrow at four. And I got a little bit confused because I had just got done looking through the camp schedule. And the camp schedule said that the first workout with the kids was the following day at 3.30. And Kobe noticed the confused look on my face, and he clarified that with a wink and said, yeah, that's four a.m. Well, as you all know, there's not a legitimate excuse in the world on why you can't be somewhere at four in the morning. So I basically committed myself to being there. And I figured if I was going to be there anyway, I might as well try and impress Kobe. I might as well show him how serious of a trainer I was. So I came up with the plan to beat him to the gym. So I set my alarm for 3.00 a.m. The alarm goes off. I quickly jump up. I get myself together, and I hop in a cab, and I head to the gym. And I get out of the cab, and it's 3.30 in the morning. So it's pitch black outside. And yet the moment I step out of the cab, I can see the gym lights already on. Even from the parking lot, I can faintly hear a ball bouncing and sneakers squeaking. I walk in the side door. Kobe's already in a full sweat. He was going through an intense warm-up before his scheduled workout started with his trainer. Not a professional courtesy.  I just sat down to watch. And for the first 45 minutes, I was shocked. For the first 45 minutes, I watched the best player in the world do the most basic footwork and offensive moves. Kobe was doing stuff that I had routinely taught to middle school age players. Now, this is Kobe Bryant, so don't get it twisted. Every single thing he was doing, he was doing with unparalleled level of intensity. And he was doing everything with surgical precision, but the stuff he was actually doing was incredibly basic. Now, the workout lasted a couple hours, and when it was over, I didn't say anything to him.  I just quietly left. But my curiosity got the best of me. Later that day, I had to know. So I went back up to Kobe, and I said, Kobe, I don't get it. You're the best player in the world. Why are you doing such basic drills? And again, he was super gracious and smiled, but he said with all seriousness, why do you think I'm the best player in the world? Because I never get bored with the basics. I never get bored with the basics. Kobe Bryant, the best player on the planet, said, I never get bored with the basics. That taught me a life-changing lesson, and that's just because something is basic. It doesn't mean that it's easy. If it was easy, everyone else would be doing it.  The basics work. They always have, and they always will. And if you want to achieve your potential in performance individually and collectively, you have to admit that the basics work, but you also have to have the humility to acknowledge that implementing them with consistency is never going to be easy. Now, I'm very grateful that this is the fourth time I've gotten to do something with omni-cell. So I know that around mathematically, about half of you have seen me speak before, which means you've heard the Kobe Bryant story before because it's one of my signature stories. And the reason I shared it again is not because I lack stories. It's not because I'm a one-trick pony. I've learned the power of repetition. Repetition, repetition, repetition. Repetition is not punishment. Repetition is the oldest and most effective form of learning on the planet, and that will never change. And I've also learned, as a coach and as a father of three, that just because you tell them, it doesn't mean they heard you. So tell them again. Just because you show them, it doesn't mean they saw you. So show them again. And just because people know, doesn't mean people do. By show of hands, how many of you have seen me speak live at one of the previous omni-cell events? Put your hands up high. Okay, so it's about half. Keep your hands up. If you have implemented every single thing that I've told you and not missed the day since you saw me speak, keep your hands up. Okay, thankfully, we don't have any liars in the building. Just because we know doesn't mean that we do. Now I'm here today with one very basic goal. That's to give you guys some tools and some concepts. So you can not only raise your game individually, which certainly is the first step, but it's so you can continue to build an unbeatable team. And in order to build an unbeatable team, you have to know what it is that you do well. You have to know what it is that separates you from your competition. And you have to make sure that you're doubling down on those things. J. Billis of ESPN is a good friend and mentor of mine. He was kind enough to write the forward to the book that you all have been given. And in 2010, in December of 2010, Duke was going to play Butler. Now this is important because previously that year was the NCAA Finals, the championship game where Duke narrowly edged Butler when Butler missed the buzzer beater. So now they were going to replay that championship game in New Jersey in December of 2010. And part of J's duties with ESPN Game Day is he goes and watches each team practice the day before the game. Well, if you follow college basketball, you know that J is a Duke alum. So he went to the Duke practice first and he goes over the day before the game and Coach K is telling the team, we are going to beat Butler tomorrow because we're bigger, we're stronger, and we are more powerful than they are. We are going to pound the ball down low, we're going to get easy layups and dunks. We're going to out rebound them and we're going to block their shots. We have the advantage because we are bigger, we are stronger, and we are more powerful. J left going, this is going to be a bloodbath. Clearly Duke has the advantage, Coach K just said so. But I need to go watch equally brilliant Brad Stevens hold practice with the Butler Bulldogs. And he goes over to watch Brad Stevens practice. And Brad Stevens says, we are going to beat Duke tomorrow because we're smaller, we're faster, and we're quicker than they are. We're going to get wide open threes, we're going to get easy buckets in transition. They're big guys can't run with us because we're smaller, we're quicker, and we're faster. And J left and he thought, I don't know who in the hell is going to win this game tomorrow. Because both teams are very aware of what they bring to the table and what their strengths are. And both teams actually see these things as their competitive advantage. Now as I've become acclimated with the Omnicell mission and culture through the other events and through what I saw today, it's very clear to me that your competitive advantage is you guys. It's your people and it's your ability to build relationships. I understand the mission of looking for autonomy and being able to take the human factor out of what it is that you're trying to deliver. And I truly commend that, I think that is remarkable. But your competitive advantage is the relationships that you all build with two incredibly important groups. One, it's the people in this room and everybody else that's a part of the Omnicell team. It's everyone on your team. The stronger your relationship with those in this room and those on your team, the more unbeatable you'll be. And then clearly, it's with those that you serve. And the stronger your relationship with those that you serve, the better and more unbeatable you guys will be. And when we talk about relationships, it's all about creating connection. It's all about fostering and strengthening your connection with those on your team and those that you serve. Now, connection can only happen if we're open, if we allow ourselves to be vulnerable, if we allow ourselves some humility. We work on our emotional intelligence and we care. Caring matters. And I know that's a major theme with you guys. We have to make sure that we keep that because caring is a choice. Caring is an act of will. You don't have to like someone to care about them. There may be someone here in the room right now that you don't particularly like. Now, don't look at them right now. That'll make it awkward for everyone. But you don't have to like someone to choose to care about them and to choose to care about the greater omni-cell mission because caring is a choice. But when it comes to connection, connection is not a one-and-done thing. Connection needs to be accrued over time through daily deposits. In 2006, Steve Nash won the first of back-to-back MVP titles in the NBA. And Steve Nash is one of my all-time favorite players. And that first year that he won the MVP, he only led the league in two statistical categories. Number one was assists. Those of you that follow basketball, you know, that means he likes to share the sugar. He got everybody else involved. Certainly the mark of a great leader. But the other statistic that he led the NBA in were touches. I'm talking about high-fives, fist bumps, and pats on the butt. How could I possibly know that Steve Nash led the NBA in high-fives, fist bumps, and pats on the butt? There was a research team from UC Berkeley that was doing an official study. And they were trying to measure to see if there was a direct correlation between showing signs of enthusiasm and actually winning basketball games.  The Phoenix Suns who Steve Nash played for were so enamored with this study that they hired a full-time intern to keep track of just Steve Nash. Now by show of hands, how many of you have had a crappy entry-level job before? Yeah, can you imagine if that was your job? Yeah, you see this guy over here? Every time he touches one of these big sweaty guys, yeah, if you could make a tally mark. In the first game that the intern recorded for Steve Nash, he delivered 239 high-fives, fist bumps, and pats on the butt. He is a furnace of human connection. Now when we're talking about the sports world where physical touches is appropriate, there's actually a physiological transfer of energy when you touch another human being. You can actually raise their level or raise their game through physical touch. Clearly we're not talking about physical touch in this domain. We're talking about, yeah, HR will make sure of that. We are talking about emotional touches. We are talking about making emotional deposits. These can be done digital, which is one of the great things about the digital interconnectivity that we have. But it's all about making consistent touches. I had a mentor of mine a long time ago teach me a concept called Ten Assist, which some of you have heard. And Ten Assist is you wake up every single morning, and you can choose to either put 10 pennies in your left pocket, or if you'd like you can wear 10 rubber bands on your left wrist, or if you're more of a fashionista you can get some nice bracelets. But you'll have either 10 pennies in your pocket or 10 bracelets on your wrist. And every time you give an assist to one of the two groups that I mentioned, someone that's on our team or someone that we serve, you take one penny out of your left pocket and you put it in your right pocket. Or you take one rubber band or bracelet off of your left and you put it on your right. And an assist is anything that you do that adds value to their life. Anything you do to make their job easier, to be a good teammate would be considered an assist. But here's the rub. You can't go home until you've given out 10 assists. You can't leave and go home and put your head on the pillow until you know for a fact that you've done at least 10 tangible things to add value and to deepen a connection with the two most important relationships professionally that we're talking about. Those on our team and those that we serve. Now that needs to be something that we make go viral. I know when we talk about social media, everyone's worried about likes, everyone's worried about clicks and views. Let's not worry about that. If you want to continue to build an unbeatable team, which you guys are doing, let's make that contagious. Let's hold each other accountable to the fact we will always do a minimum of 10 things to deepen the connection in the two groups that matter most to us. And if we can focus on creating those type of connectivity and we can focus on making sure that we are creating connection and building relationships because we know that is your competitive advantage, then you'll be able to move on and graduate to the three steps that are required for building an unbeatable team. And number one is role clarity. Number two is accountability and number three is communication. If you guys can come close to mastering communication, accountability, and role clarity, you will continue to separate yourselves from everyone else. You will continue to move forward towards your mission and you will continue to work towards being an unbeatable team. So, let's unpack each of those a little bit. Let's talk about role clarity. You know, I've seen Jeff speak a few times and I love his analogy about a NASCAR pit crew and how that represents the true teamwork and everybody doing their role. I don't watch a ton of NASCAR, but I know enough to know that every single person on that pit crew has a very specific role and a very specific job and they need to do that specific role and that specific job to the best of their ability. And if they don't, the whole thing can fall apart. If any one single person on a pit crew does not do what they are supposed to do, the whole thing can fall apart. And I want each of you to view your role in the exact same light. See, similar to a pit crew, I believe that a team is very much like a jigsaw puzzle. That goes back to the fact that I've got three young children. So we've done a lot of jigsaw puzzles over the last couple of years, especially on rainy and snowy days. But here's what I know about a jigsaw puzzle. Every single piece matters. Every single piece matters. If there is one piece missing, you can't finish the picture. And if you're the father of eight-year-old twin sons and a six-year-old daughter, if you get to the end of a jigsaw puzzle and there's one or two pieces missing, there's a crying fit. I'm pulling off couch cushions. Everything I can to find the missing pieces because I want to finish that picture. And each of you has to take that much pride in your role. You have to realize that what you do for Omnicell is vital, it's important, and it needs to be appreciated by everybody else. See, when we look at roles, and first of all, you have to understand this. When it comes to the greater good of a team or an organization, your role is not always what you want it to be. Your role is what the team needs it to be for the team to be successful. Now, in a perfect world, there would be as much alignment as possible between what you love to do and what you're good at. That would be the ideal role for you to spend most of your time doing what you love and what you're good at. And that would be a perfect world. But as you all are well aware, we live in a practical world, so it's not always perfect. So you being able to say that even though this isn't my favorite thing in the world to do, I have other people that are counting on me to do this to the best of my ability. When you get folks to buy in to do that, that's when we create something special when it comes to roles. And each of you needs to think well above and beyond just knowing what your role is.  I know you know what your role is. But where you have to actually ask yourself a question when you look in the mirror, is are you truly embracing that role with everything that you have? Your power to star in your role. I know there's big roles, there's small roles, there's all sorts of different boxes on the org chart. I get it. But all you have to worry about is guard your yard. In your yard, are you doing everything you can to add value to the North Star and the mission that you all are collectively trying to accomplish. In order for you all to truly get there and to get there as efficiently as possible, you need every single one of you to be able to look in the mirror and say, yes, that's what you do. Now let's talk about accountability. Holding someone accountable is not something you do to them. It's something you do for them. And it's really important to have that mind shift. Holding someone accountable shows them that you care about them. You're basically saying, I believe you're better than what you're showing me. I know you're capable of more than this but I'm not going to let you slide on that. Whether you're a parent or a leader within the company, holding people accountable shows them that you care. In order for you all to reach that North Star, you have very high standards and the key is not just having high standards. Anyone can have high standards. Do you hold each other accountable to executing those high standards? That's the difference between an average team and a good team, a good team and a great team and a great team and an unbeatable team. You have to hold accountable to accountability. But here's the other difference. In very average organizations, accountability is simply vertical. They look at the org chart and say, I'm in charge, you report to me, I hold you accountable. You're in charge of these people, you hold them accountable. That's very basic. If you guys want to be unbeatable and continue to rise to be elite, we have to have horizontal accountability which means everyone in the room can hold everyone else in the room accountable. We're throwing out the org chart because it doesn't matter where you fall on the org chart when it comes to being held accountable which means you don't wait for me to tell you to do what you're supposed to do. These two guys to your right and left are going to tell you and hold you accountable to make sure that you're doing it. And how do we get that type of buy-in and believe-in in addition to the care factor? Is we simply have to ask permission. Now I know that at a company of this size it's not realistic for you to go ask this to every single person in this room but in theory here's what you need to play back. You should be able to go up to any person in the company regardless of where they fall on the org chart, regardless of their role and you should be able to look them in the eye and say, do you give me permission to hold you accountable to the standards that we've set to live out, to follow this north start? Do you give me permission to hold you accountable? It's a binary question, it's a yes or a no. Anyone that answers no to that I'm not looking to do a mass firing but I would strongly consider that that person shouldn't be on the team because anyone that's not willing to allow themselves to be held accountable for the greater good that's an act of selfishness and we need to make sure we eliminate and eradicate any type of selfishness if you guys want to be unbeatable which means in essence every single person in this room should be able to look at anyone else in this room and say yes you can hold me accountable yes, I want you to hold me accountable yes, please hold me accountable so that I can be the best that I'm capable of and we can be the best that we're capable of and once everyone is bought in and given that permission then we've taken the personalization out of it it's not personal so it goes back to it doesn't matter if you like or dislike someone it has nothing to do with that it has nothing to do with being accountable to the standards you've set to go after this Goliath of a goal that you all have and accountability is crucial and the vertical and the horizontal accountability combining those two and actually giving permission for people to hold you to the highest standard possible once again is the difference between a good team and a great team and an unbeatable team now let's talk about communication when we talk about communication most people immediately relegate that to the talking portion I mean, I'm a professional speaker I get paid to actually talk but the real goal is not in the talking it's never in the talking the real goal it's in the listening anything you need to know to strengthen a relationship or to have a stronger connection with those on your team or those that you serve it's all in the listening I talk to sales groups all over the world and one of the very first things I tell them is telling is not selling like if you're looking to sell you don't tell people don't worry about all your features and benefits and all that stuff what you need to do is you need to ask insightful questions and when you ask insightful questions and you actively listen to the answers they give you back then you can drop the breadcrumbs wherever you want an elite sales professional never, ever convinces anyone to buy anything they ask the right questions and the prospect convinces themselves and you can only do that through active listening what is active listening it's listening with the intent to connect it's listening because you're trying to learn something it's not doing what the vast majority of people do which is listen just because you're waiting for your turn to talk active listening has everything that we need Arthur Blank the founder of Home Depot back in the early days when they only had one or two stores he would go to the flagship store every Saturday morning and he'd have a clipboard with one of those old yellow legal pads and a pen and every time somebody walked out of Home Depot empty handed they didn't purchase anything they went into the mega super store and they left empty handed he would go up and start to ask them questions why didn't you buy anything did we not have what you were looking for could you not find what you were looking for did you need some help but no one gave you customer service he wanted to find out why someone could go into a store that technically had everything needed for home improvement and leave empty handed and he would take note after note after note and when he started to notice some trends he would start to make some changes if everyone that was coming out said they couldn't find the hammers then he made sure he put the hammers where everyone could see them the moment they walked in the store but it all came through listening and the ability of having the humility and openness to ask questions and figure those things out now another thing about communication that's vital especially when we're talking about building connections you're always communicating even when you don't think you're communicating you're communicating and I'm not just talking about the nonverbals I'm not just talking about eye contact and body language and tonality that stuff counts but it also goes in your actions I'll give you a perfect example if you delegate something to someone on your team in this room I'm not talking about a menial task like take out the garbage I'm saying we're working on a project and I need your help on this I trust you I believe in you I know that you can do this as well as I can do this and I need your help that will strengthen a human connection conversely what message do we send unconsciously when we micromanage someone I give you something to do and either literally or figuratively I stand over your shoulder while you do it what am I telling him now I don't trust you in fact I think you're such a moron that if I don't stand over top of you this is not going to get done do you think that builds or erodes a human connection it erodes it and I know that that would come from a genuine place that you might be a little bit of a perfectionist and you have the expertise to make sure it gets done the right way and I want to kind of help you along but we have to realize what we're actually communicating when we don't think if you all can continue to do the internal work and the collective work to work on your communication learn to have vertical and horizontal accountability and everybody in the company knows their role, embraces their role stars in their role and everyone appreciates everyone else's role you'll be on your way to being an elite unbeatable team now I've noticed that you guys are being such great active listeners I've noticed that no one's heads exploded yet and no one had kind of that Tom Cruise on Oprah moment and jump up and shout and there's a reason for that I haven't told you a single thing yet that you don't already know intellectually or intuitively I have not told you a single thing that you don't already know but as I told you earlier there is always a gap between what we know and what we do and for you to be the best version of yourself possible in any area of your life and collectively for you all to be an unbeatable team we have to be diligent and focused on closing that gap the example I always use between what we know we're supposed to do and what we actually do I always use health and fitness and wellness as an example you guys are a sharp group you're high performers, you're high achievers so I have zero doubt that if right now I ask you in your notes to write down the healthiest foods that you know of you guys would generate a pretty good list in fact most of you would write down a lot of similar foods then if I ask you just to shout out how many hours of sleep are you supposed to get every single night you guys could shout that out in a split second most of you would shout out the exact same number just to etch out what a physical fitness workout program should look like you don't have to send it in to men's or women's health just roughly how many days per week what should you do and how long a session should be I have no doubt that you guys could all etch that out but here's where we're going to look for a performance gap when it comes to health and wellness and vitality and longevity is I ask you to look back down at your notes and I ask each and every one of you a series of binary questions what are the foods that you eat is that the amount of sleep you got last night and are these the type of workouts you do regularly it's a series of binary questions if your answer to those is yes this is exactly what I eat that's how much I slept last night and I actually did see two or three people in the gym this morning that I know were omni-cell people and say yeah I actually got up early before today's events to get my workout in that just means when it comes to health and fitness you have a performance gap that's awesome if your answer is no I don't eat this stuff I can't remember the last time I got this much sleep and I sure as hell wasn't at the gym early this morning that just means when it comes to health and fitness you have a wider performance gap and I don't say that to make anyone feel bad and I don't say that to call anyone out I say that simply to shine the light of self-accountability on the fact that you know what you're supposed to do you're supposed to be doing it which then of course begs the question how could a room of high performers high achievers and to be safe relatively intelligent people not do the things that they know they're supposed to do how could that be it goes back to how I started this talk because it's not easy if doing all of that stuff was easy every person in the room would already be doing it but it's not and we are also as human beings we have to recognize that we are creatures of habit we love our habits and we love our routine Duke University did a study and they found that 45% of everything we do during our waking hours is habitual that means almost half of every single thing you do from the moment you wake up to the moment you go to bed your pilot is on cruise control is done unconsciously so we can clearly see how important our habits are but we also love our habits because we've grooved these patterns of behavior and it's where our comfort lies and anytime you ask someone to change a behavior or change a habit it leads to discomfort and most people and I believe it's even wired in our DNA do everything possible to alleviate discomfort we try to resist and run from discomfort at every chance we get this is where I consider myself incredibly fortunate spending 20 years as a basketball performance coach because discomfort if I had a player come in or a team come in for a workout discomfort wasn't a nice to have it was a requirement it was a necessity my goal with every single player that I worked with was to take them right to the edge of that cliff of discomfort now I was never supposed to push them over but I was supposed to take them to that edge of discomfort because discomfort is a prerequisite to growth it's a prerequisite to everything it is that you want to achieve so we have to be able to flip the switch and change our mindset I cannot do anything about the fact that if I ask you to change a habit that there's going to be some discomfort involved there's nothing we can do about that so the sooner we can accept that as fact the better off we can be but what we can all do is change our relationship with discomfort and view it as the prerequisite that it is and say that this is just a path in order to get where I want to go so I understand there's going to be discomfort and I'm willing to embrace it I wouldn't do this partially because I'm a nice guy but mostly because I don't even think there's enough space if I had you guys all get down right now and start doing push-ups what would most of you do if your push-ups started getting hard when your arms and chest and core are burning and shaking and are on fire what would 99% of you do if you were a sane human being you'd stop right of course you would, you'd stop so that the discomfort can go away but those of you that do work out regularly the three or four folks that I saw this morning at the gym you know three or four out of 300 what you do after the burning and the shaking starts those are the ones that make you stronger those are the ones that are actually getting you where you need to go so we have to learn how to make sure that we are embracing the discomfort because the discomfort is temporary the new habit or behavior can be permanent I had a chance to meet Kevin Durant when he was 15 years old we're both products of the DMV area DC, Maryland, Virginia area and I had a chance to see him play up close and personal when he was 15 and I watched him play for about five minutes and I was able to make the following assessment number one this kid loves to play basketball he was working his butt off but boy he was smiling the entire time and playing as hard as possible number two, man he's fundamentally sound his shooting technique and his footwork were pristine for somebody that was only 15 years old number three boy he has a really high basketball IQ he understands the game on a cerebral level that most coaches don't but number four let's say Kevin was a little bit slight of frame he used to get really pissed off when I would call him skinny but let's be honest when Kevin would stand sideways you could physically see his heartbeat like he was super duper skinny so it was pretty obvious to me basketball performance coach a strength and conditioning coach that he needed what I had to offer and I was excited for the opportunity now it took a lot of persistence in fact it took months of constant calls trying to beg his wonderful mom Wanda to let her baby boy come in for a workout because he had never at that point touched a weight and finally after about three months of persistence she finally allowed him to come in for a workout yesterday we met at a gym in PG county and I had this immaculate workout I thought it was the greatest workout ever designed and in about 30 minutes I got a little bit over excited in about 30 minutes I murdered him I was the hammer and the nails I told Jesus the moment ago you're not supposed to push him off the cliff I gave him a running jump kick off of the cliff and in about 30 minutes Kevin was 6'10", 180 pounds at the time so he was more coiled up like a snake but he was sweating profusely and his muscles were twitching and Kevin has always been short on words he's never been incredibly outspoken he was very quiet during that entire workout in fact he didn't say two words so I had no idea whether or not he actually liked the workout so I simply asked him I said hey young buck did you like that workout and I remember him looking up and as serious as can be he said no I didn't but I know this is what I need to do if I ever want to play in the NBA so when can I see you again coach I remember being blown away by the maturity of a 15 year old young man who understood that he was going to have to make a change and that change was going to come with a tremendous amount of mental, physical and emotional discomfort but it was a sacrifice that he was willing to make and knew that he needed to make if he wanted to get where he wanted to go now most analysts have him right now nipping on the heels of being the best player in the world and then there's no way if I'm being honest with you all there is absolutely no way I could have ever predicted that at his age but I can also tell you now I'm not even slightly surprised because when you can mix that type of talent with the ability to run towards discomfort and not run away from it it's just incredible things happen and that's when high performers and high achievers really come into their own so we have to be willing to embrace change now there's a foundational principle that ties all of this together so we've been talking about mastering the basics we've been talking about finding your competitive advantage and what makes you unique and doubling down on that we've talked about how important it is to have role clarity and to have communication and all of these are within the confines of strengthening connection so we can create relationships the only way you can do any of those things to the best of your ability and in my opinion the only way you can ever come close to achieving real happiness fulfillment, success, or significance is by being in the present moment in any era of your life if you want to win the moment you've got to be in the moment and that is much easier said than done with the bombardment of digital distractions that we face every second of every single day being in the present moment is for me without question as a 43 year old father of three and a private business owner is without question the biggest challenge that I face every single day is being in the present moment and the short definition of being in the present moment is be where your feet are wherever your feet are make sure that's where your head and your heart are as well and this is absolutely crucial to creating the connections that we've already established we need to be able to achieve that north star if you want to strengthen the connections with the people in this room you want to strengthen the connections with the people you serve with your life significant other children, neighbor it doesn't matter the very first step to doing that is being in the present moment I've done this long enough to know especially with an audience of 300 I don't know what the actual percentage is I could make something up on the spot not every single person in this room right now is fully present your feet are in the room but there's some of you right now your head and your heart are not in this room thinking of something other than what's transpiring right now and I don't say that with judgment and I certainly don't take any offense to it I just know for a fact that attention is the number one currency we have it's the number one gift you can give another human being is your attention in the present moment it's the number one gift you have to give and that's because time is our most precious resource but each of us were born an hourglass got flipped over and sand started falling and in 43 years of walking this earth I've figured out there are three indisputable truths about time and there are three indisputable truths about that hourglass number one, none of us has any idea how much sand is at the top none of us do tomorrow is not promised tomorrow is not guaranteed number two, we can't stop the sand from going to the bottom you can't pause time you can't stop time and number three, once the sand hits the bottom it's gone and it's gone forever you can't get time back and you can't relive time now you can learn from the past and if you're wise you will learn from the past but you can't relive it and because time is our most precious resource then that means our attention in the present moment is without question you talked earlier about you're always communicating something if you give someone your full undivided attention you are unconsciously telling them that you are important to me that I care about you that what you have to say is something that I value and there is no greater glue in the world to forge a relationship or a connection than that so we have to make sure that we're constantly aware of and reminding ourselves to be where our feet are in fact for me and this was a major issue in my life for years I have a point of awareness now that usually within 10 to 15 seconds I can tell if I'm not present if you and I are having a conversation and I start to zone out it takes me about 10 seconds at maximum to realize that I'm not present and I need to get back to that and that's my trigger that's what I say to myself be where your feet are Alan I don't say it out loud I say it to myself so that I get back to the present moment and give you the attention that you deserve but let's unpack it even more that was the short definition be where your feet are let's talk about the expanded definition number one is you learn how to focus on the next play number two you learn how to focus on what you can control control the controllables and number three you learn to focus on the process if you can focus on the process if you can focus on what you can control and you can focus on the next play then you'll be where your feet are so let's talk about next play in my basketball journeys I've been around some great players and I've been around some great coaches one of the best coaches that I've ever been around is Mike Jones he's a coach at Demathe Catholic High School a very very good high school in Washington DC area we've had multiple players go on to the NBA and one of the things that coach Jones does at a remarkable level is he teaches our players the concept of next play and if you ever were to sit with an earshot of the bench during a Demathe game I kid you not you would hear coach Jones say and make this hand motion next play sometimes over the course of a high school basketball game now why does coach Jones want his players focused on the next play it's the only one they can do anything about they can't do anything about the play that just happened you just turn the ball over it's okay next play you just missed the wide open dunk I know, I know the referee missed the call it happens occasionally in high school basketball next play because the missed call or the missed dunk or the turnover is over there's nothing to do about it so the quicker you can move on to the next play and be in the present moment is the quicker you'll be at your maximum but what happens is players get worried about the things outside of what they can control they have bad body language and they pout and they get in their feelings because the referee missed the call oh I can't believe I missed that shot I just turned the ball over and in the four or five seconds that they pout have bad body language and they're in their feelings that's usually accompanied by trotting back on defense and in the fast paced game of basketball and absolutely in the fast paced game of life and in business the four or five seconds that you choose to be in your feelings and you choose to jog back at the demathal level it's two points on the other end because the player you're guarding sprinted the floor and made an easy layup so you missed a shot or you turned the ball over or the referee missed the call and then you chose not to be in the present moment and now you went from a two point mistake to a four point mistake and we can't have that we have to move on to the next play it is my belief that Steph and Curry will go down in history as the greatest shooter that the game has ever seen and yes he has flawless mechanics and he has insane depth perception coordination and neurological hookups but one of the reason he'll go down in history as the greatest to ever do it is because of his next play mentality this does not happen very often because he's that good but you guys know the analytics that are available now in the NBA it's incredible so you can look up the data there are a handful of games each season that he'll start the game 0 for 7 he'll miss his first 7 shots it does not happen very often because he's really good but the reason he'll be the best to ever do it is because he'll shoot that 8th shot as if he made his previous 7 he doesn't let what happened in the past affect what's going to happen in the present he's able to wipe that slate clean in fact that joker could miss 20 shots in a row and the games tied with 2 seconds left and he will beg for the ball because he knows the next shot is always good he never ever lets previous performance have a negative impact on current performance that is the next play mentality and you can look at that through any lens that you want through a business lens, through a life lens anything that you want when it's done it's done and you move on to the next play now let's talk about focusing on what we can control control the controllables there's actually only 2 things in the entire world that each of us has 100% control over 100% of the time there's only 2 our effort and our attitude that's it now there's lots of other things within our sphere of influence and I'm a believer that if you take a little bit of effort you take a little bit of attitude and you mix them together you have preparation or you take a little bit of effort and a little bit of attitude and you mix them together you have enthusiasm so there's other things that we can have a very strong influence over but if you brush away everything else it all comes down to our effort and our attitude let's look at effort first this one fascinates me because every sane human being I've ever met will acknowledge the fact that working hard is a choice in fact if I ask you guys right now is it your choice to work hard I would imagine I'll see some heads not but here's what I also find fascinating very few people own the fact that means not working hard is also a choice there has to be another side to that coin you cannot have one without the other but what happens going back to accountability when you hold someone accountable for not giving the best effort they were capable of if they're like most people they start to come up with excuses well I was sick I was tired I was hungry I was this I was that effort at any given moment in time is 100% your choice and if you want to be a high performer and a high achiever individually and collectively then you have to rewire yourself to make the consistent choice to give the best effort possible at all times that's very basic right you guys know I can tell by the look in your eye we all know that's not easy giving our best when we don't feel like it when it's not convenient when we don't want to is incredibly challenging which is why most people choose not to do it but our effort is a choice and that's the number one thing that you can hold everyone else accountable for when we go back to the vertical and horizontal accountability man I know you were capable of giving a better effort come on man we're all counting on you I know you can do better than that once again that's a sign of caring that's the effort side now let's talk about the attitude side we don't control the vast majority of stuff that goes on in this world that was a tough pill for me to swallow because I'm somewhat of a control freak but we control how we respond to it how many of you have children how many of you were children yeah so at some point you can probably relate to the fact that you either had a parent say this or you've said this yourself I just bust out laughing when I say this to my kids now like you don't control Luke you don't control what your brother Jack does but you control how you respond yes I know you didn't want him to bite your neck but there's nothing we can do about that now so how you choose to respond and whether you punch him or bite him back now that's on you so the world is always going to throw things at us and there's going to be feedback given to us at all times because life is nothing more than a series of at bats everything we do is just another rep it's just another at bat and every at bat we get gives us some type of feedback and if you want to be a high performer if you want to be a high achiever if you want to raise your game then you have to choose to take every single thing that's thrown at you and use it in a way that serves you and moves you forward instead of choosing to use it in a way that cripples you and moves you back in and of itself please know is completely unbiased it's sterile it's not positive or negative it only becomes positive or negative when we as human beings choose to associate emotions to it when you can depersonalize it and step away from all feedback from a personal standpoint and say what from this can I use to make myself better and choose that consistently as opposed to how can I use this to regress and move back in your way to being a high performer and the choice is always always yours basic right definitely not easy when jack bites Luke's neck for him not to turn around and punch him is a really really hard decision for an eight year old to make but it's one that I'm trying to condition them to understand that that is not a knee jerk response that is a choice now let's talk about focusing on the process we talk a lot about that in society because it's a buzz word and the reason people talk all about the process instead of the outcome is because it's true we can't guarantee any outcome in this world but we can greatly increase our chances by sticking to and living in the process for those of you that have seen me speak before I've been very open about the fact that I'm not handy I'm not good with tools I can't build stuff, I can't take stuff apart but I'm not very good at putting stuff back together I believe that's a gene passed down genetically and my parents did not give that to me when something in my apartment breaks yeah I pay someone to come fix it or I just live with the fact it's going to be broken forever because I can't fix anything however despite the fact I don't have any handyman skills I have full confidence that I can build a sound sturdy brick wall and the reason I have that confidence is because over time I've conditioned myself to trust, respect and appreciate the process I'm capable of picking up one brick and setting it exactly where it needs to go and then I can pick up another brick and I can set it exactly where it needs to go and as long as I choose to stay focused on each individual brick there's a really good chance this wall will take care of itself but the moment I stop focusing on each brick and I start thinking too big picture how long is this wall going to be how tall is it going to be and I start worrying about everything else inevitably I'm going to lay sloppy bricks and that's the only guarantee that I can make you if you lay sloppy bricks you'll never ever get a sound sturdy wall so you have to learn how to live in the process Jeff was talking about mission is greater than commission well that's another way of saying it's about the process if you guys focus on the mission of what Omnicelle is created to do and the mission of what your specific role is and you do that to the best of your ability the commissions will take care of themselves you don't have to focus on those so stay mission driven so we need to make sure that we focus on the process we need to make sure that we focus on what we can control and we need to make sure we focus on the next play if we can do those three things routinely you'll be as close to living in the present moment as possible two summers ago I got invited to run a charity endurance event at the home of Jesse Itzler and Sarah Blakely do you guys know who Sarah Blakely is? she's the founder of Spanx it's a women's undergarment company but she's also the youngest self-made female billionaire in the world she is one of these sharpest human beings that I've ever met and her husband Jesse is equally remarkable he's a professional speaker and he's an author and he's an endurance super freak and what they did was they invited 70 of us up to their house in New Fairfield, Connecticut to run a charity event now I played college basketball I'm a basketball guy which is a short burst high intensity sport there's a lot of starting and there's a lot of stopping it's not much of an endurance component I've never been an endurance athlete so I knew that this was going to be challenging I had no idea how challenging it was going to be you see the backyard to their New Fairfield, Connecticut home has a patch of grass that's 85 yards long so just shy of a football field and that patch of grass is at a 40 degree slope for the three or four of you that were in the gym this morning if you hopped on the treadmill you'll know that a conventional gym treadmill goes up to 15% and if you've ever put that thing up to 15% and tried to go for a brisk walk you feel like you're going to fall off the back of the earth and that's 15% this was 40% and it was 85 yards long and our task for the day this event was to run up and down this hill 100 times yeah it was called hell on the hill and that it was that it was at around rep 70 I remember vividly right around rep 70 I could feel blisters forming under each big toe I could feel throbbing in my knees and my hips and my back and I apologize for the visual but I had some chafing going on that was absolutely out of this world and each of us has that little voice inside of us that little voice some call it reason some call it kind of the angel and the devil but that little voice that says things like why are you doing this there's no way you can do 30 more of these what are you a dumbass why did you think you could go up and down this hill 100 times you need to quit now as you've probably gathered I'm a rather positive and optimistic guy so that little voice very rarely comes out in my life but it came out that day around rep 70 and it wasn't tapping me on the shoulder or whispering it was screaming telling me to stop now it just so happened that one of my good friends was also running and we were on about the same pace his name's Steve Wojahowski and he's a Duke basketball legend and he's the current coach at Marquette really really tremendous guy and I knew that we were on about the same pace so I guess just to commiserate and misery I asked him how many reps he had left and he smiled which really pissed me off yeah, it's exactly what I said one rep there is absolutely no way you only have one and then he cut me off and he said I have one rep 30 more times that is the definition of living present you don't worry about the 100 you just focus on the next rep you just got to get up and down that hill one more time baby one more time you don't worry about your toes and your back and your chafing situation you just focus on your attitude and you focus on your effort and I was a performance coach so I was not a mathematician nor was I a statistics major but even I know that you can't get to number 100 till you go through number 71 so you have to stay present and as I said earlier if you want to win the moment you have to be in the moment and that gentle reminder to get back to present is what allowed me to finish all 100 reps of four hours of continuous running up and down the hill but being present and remembering those three things is absolutely what did it now before we wrap up this is usually the point where I'm going to tell you guys a number that you can text if you want to get the notes from this talk so if you want you can either write this down or you can pull out your phones right now I know some of you have been itching to do that dying to do that and those of you that did pull them out if you want to see it please realize your big old face lights up when you hold your phone in front of it so I saw you if you text the word bonus to 66866 66866 the word bonus and because we know I'm a fan of repetition one more time bonus to 66866 you'll get automatically sent a pdf with 10 pages worth of notes and normally at this time I tried to promote my book I would tell you guys that I just had a book come out and how bad I want you to go to the website and get it I don't need to do that because your leadership was so kind to invest in a book for you all and I believe you have them now and because I'm not bashful about shameless promotion can you hold up your book for a second so I can get a picture yeah laugh all you want I'm taking a picture of this and I'm posting it later actually we'll do a video look at that thing up pretend like you're happy you got it pretend like you're going to read it and here we go look at you guys alright that makes me really happy thank you very much now let's end with with this I started my talk telling you about the Kobe Bryant Skills Academy that was not far from here right in L.A but what I failed to tell you is that one of the college counselors at that camp was another gentleman that I've already referenced and that's Stefan Curry but this is in 2007 so this was after his freshman year at Davidson and this is before he became the Stefan Curry that the entire world is infatuated with now in fact he was so unknown in 2007 that the coaches didn't even call him by his name they simply called him Dell's son because his dad played in the NBA for a dozen years yeah that's Dell's son over there that's Dell's boy over there but what he lacked in stature and what he lacked in resume he more than made up for in a few ways but the most remarkable way was at the end of the very first workout you realize this was an intense mini camp we did two workouts a day for three hours each for three or four straight days this was intense and at the end of the very first one just based on mere proximity I happened to be standing near him and I was wearing one of those goofy shirts I think that said staff on the back and he said well you rebound for me leave the gym until I swish five free throws in a row swish five free throws in a row if you've never personally shot a basketball let me tell you that is an incredible standard a swish by definition is the perfect shot it doesn't touch the rim it doesn't touch the backboard it gets its name from the sound it makes when it goes nothing but net which means he could swish four in a row hit a little bit of the rim on the fifth one it still goes in he's still five for five he's still mathematically perfect but that wasn't good enough to him he would start over and if memory serves it never took him longer than 12 to 15 minutes to swish five in a row as I told you earlier Stephen Curry will go down in history as the greatest shooter that the game has ever seen not by accident not because his dad played in the NBA because he's willing to hold himself to an unparalleled standard and that is the thought that I will leave you all with that the standards that you set today both individually and collectively they will determine where you'll be tomorrow and with that I thank you guys very much thank you


Live from Nashville, Tennessee, it's theCUBE.  Welcome back to Nashville. You're watching theCUBE at Commvault Go, our first year at this show, the third year of the show. I'm Stu Miniman, co-host Keith Townsend. Happy to welcome to the program Chris Powell, who's the Chief Marketing Officer at Commvault. Thanks so much for inviting us to the music city and your party. Oh, we're glad to have you guys. Thanks for being here. All right, so Chris, Commvault, I really like what I've seen at the show so far. You made a statement that really resonated with me yesterday. You said, look, this is a 20-year-old company, but it's very different than it was. We know cloud and AI and all these things are kind of changing. Things like ransomware and GDPR are hot in the data world. When we look at our research, data is at the center of everything. So, you know, what's the brand of Commvault? As we think of a company that has lots of customers, but been going through its own transformation, how should we be thinking of the company? I mean, I think what we're trying to do with Commvault is make sure that we, there's sometimes in marketing where you end up in a place where it's either, it's perception is driving reality or reality is driving perception. And Commvault's in that transitional period where it's more about reality that we need to use to drive that perception, because there's some old perceptions. And as you said, in any company, especially in the tech space that's 20 years old, you end up in a place where there's a lot of different perceptions of you from days gone by. Those can be about pricing, they can be about the usability of the product, the different technology innovations that you've had because you have such a long history to it. So we sort of need to continue to shift that and shape that as we go forward. And, you know, for us, the Commvault brand has really evolved into, Commvault is about being data experts and helping our customers be data experts. And as you said, it's, you know, data is the new oil, data as we said at the show this morning, the new water. And it's definitely sort of this space where everybody's recognizing what's happening. But it's such early days in this world of data that's changing everything around us. Yeah, we have a friend of the program, Alan Cohen, that said, here's the challenge in IT. Used to be that IT was the always been no. And then you go to the procurement people and they're really slow. And Chris, you know what we need everybody to do? We need them to go. So I really liked the branding of the show, probably not where you came up with the term, but you've got 2,000 people here. The show floor, I've been to five or 6,000 person shows that have a smaller expo hall here. You've got customers with Boost, you've got partners with Booth, you know, Nashville's got a great energy. So for people that haven't come here in person, give us a little bit about, you know, why Nashville, what you hope to accomplish with the expo, the flow, and then the show. Well, the why Nashville, and a lot of what we're trying to get with is we've all been to probably one or two too many conferences in other cities that we won't name here because I love those other cities too. But what we've done in our partnership with the Gaylord Hotels, which is a great customer of Commvaults as well, is trying to find just venues that are a little bit more interesting and unexpected and different, that it was all part of the plan as we were coming up with this is to really project Commvault in a way that we believe really was more about our image. Towns like Nashville, last year we were in Washington, DC. It's, they're great representations of what we're trying to do in the market. I was with people last night and they said so many people said they'd never been to Nashville. And this is a great town and it really represents our brand well. So Chris, 20 years, 20 years of data, there's companies that are just waking up, realizing that they have this asset locked away in there, whether it's on tape, on media that's sitting inside in some random storage facility, but they have this asset that they can now unlock. What's the central message you want these customers to know about Commvault and your ability to help them to unlock that data? Yeah, so Keith, it's so true in that when you talk to people who are more on the data scientist side of things, it's this understanding that usually the very well-paid data scientists struggle with just a couple of very basic things that they don't want to struggle with and it's not even what you pay them for. Can I get access to the data? Is the data all brought together in a form that I can really now serve it up, use it, get value from it? And as Commvault's been sort of developing and expanding our overall portfolio, it's really trying to address both of the issues of if you're someone who's responsible for data in your organization, you have a bit of a challenge on an ongoing basis. You need to make sure the data is protected, so it's a cure, it's available when you need it, but it's also that you can serve it up and you can get value from it. And the portfolio that Commvault's really been refining and introduced this past July and continued to introduce things just this week is made up of products that both enable the protection of that data, but also serving that data up, the Commvault Activate product line and the portfolio that we're starting to introduce now is all meant to try to drive value out of the data. And you're so right in that, I was talking to some of our, we have a great expert in AI that's going to be with us tomorrow, YY Lee, who's also one of our board of director members, and she was just talking about how so many companies, as you said, have locked that data away. It's not available to them, and now they're bringing in these data scientists, and their job is to try to find value in that data, but they can't get access to that data. So this is a very straightforward challenge that we're trying to help our customers with. Chris, I'd like you to take us inside your customers, because when I think about five or 10 years ago, backup is usually a storage person. It's like, okay, how do I have it? Do I have a backup window? Got to worry about recovery, something we would look at. But when you talk about data, you talk about data scientists, we're going up the stack. How do I use analytics and everything? Is there a CDO in my organization that worries about that? Coverage and compliance are board-level discussions. So bring us through, where are you talking to the customers? Is there kind of the traditional customer and the new customer? How that impact your whole field? It's a big broad question. We don't have a ton of time, but yeah. The way that I usually look at it is, you can almost come at this from two different directions, but you end up telling a very similar story. It's just almost the order of operation that you tell it. What I mean by that is, in the world of the folks who are really responsible for their virtual environment, their physical environment, and backing it up, you can talk to them about what they need and their desires in terms of the strongest backup and recovery. But then eventually, pretty quickly, find yourself talking about a better understanding of what that data is, so that you can apply your policies against it, so that you can ensure your compliance, and then eventually to be able to serve that data up for more higher value needs of your organization. And if you end up speaking to someone often, it's a more senior IT person in an organization or even all the way into the CEO's office, it's sort of just almost a different direction you go. You want to talk about how you can get value out of your data, and in order to get that value out of your data, you need to be able to understand truly what it is, where it is, who created it, who has access to it, and then eventually you find yourself to, is it protected? So it's a very similar story, but if you go to a CEO and you start with backup, they don't really want to talk to you, and if you go to a backup administrator and start talking about the value of data, they don't really want to talk to you. But what we've come to realize is it's the same story, just told in a different direction. So talk to us about bridging that gap, where at Commvault Go, 2000 people, over 150 sessions, guys have been pretty clear, this is an educational event. How do you help bridge the gap with such a large difference of users? You have over 500 partners attended the partner session, you have customers from the backup admin, all the way up to the data scientists and even executives that have to make these decisions. How does Commvault Go help bridge that gap? So in a lot of ways we use data, so we're, as the old saying goes, eating your own dog food kind of thing, we're using data from the previous conferences, and always refining this. There's 182 breakout sessions that occur over two days. There's what we call 30 and 30, it's 30 structured labs and 30 hands-on labs that you can sort of experience while you're here at the show. There's a lot of mini-sessions, so there's the theaters that hold 120 people and then there's the theaters that hold 15 people. And through a lot of the technology that shows now, the mobile apps, you can really refine what you want to experience at the show, to meet the expert sessions. We have our developers here. The first year we did this, I wasn't sure how this would work, but we brought about 10 developers for meet the expert sessions. The next year we ended up bringing 20, and this year we brought 40. 40 developers and engineers are here to have whiteboard sessions and just sit and talk to people. So it's a, we've really defined, defined to find, sorry, this show in a way that looks at the audience first, and from a marketing perspective, I can tell you that when we came into this, nobody wants to be marketed to in this industry. They want real information, and what Commvault Go has been about is real information. It's, we talk about the reality driving the perception. Commvault is strong in reality. It's, that's our reality. We just need to be able to communicate that, and we use this show to make sure we're doing it, and not selling to people. We're here to provide real information. Chris, one of the things actually surprised me. The portfolio's broader than I expected, and part of that, you had quite a bit of hard news, what I mean by that. You announced quite a lot of products, everything from the as-of-service through the Commvault. Activate standards, appliances. There's a whole lot of things there. We're going to have a lot of your team on to go through that, but you know, give us what, you know, when people walk away from the show, what you want them to know about Commvault, the announcements. Yeah, yeah. So, I think the big, there's so many different pieces, you're right, they have come from the show. Very tangible, specific things, new product line around Commvault, activate what you can utilize that solution for in terms of understanding your data, things like sensitive data governance. Then you get into the Commvault appliance and the extended appliance offering. We've taken the start of the appliance. It was just in its initial forms last year at this time at the Lascaux conference, and then extended that this year with a larger appliance offering as well as a smaller. And that's just a testament to how these things are being adopted in the market and the amount of customer uptake we're beginning to see on it. And then when you look within our product portfolio, we've tried to make sure that some of our foundational products like Commvault complete backup and recovery, that's been a big change for us recently in terms of offering what we consider to be, in the terms of the name, the most complete backup and recovery solution. And what that was is an answer to the market. Over the last 20 years, and it's not just Commvault, the whole market started to disperse their backup and recovery products. If you wanted backup and recovery, you had to go out and buy 10, 15 different products. You had to piece all these different things together. And what we realized is that what customers were really longing for was something that really brought this together so that they stopped spending all their time trying to figure out how to piece together a backup and recovery solution and started spending more of their time about how to get value out of that data. Yeah, as your CEO and COO said on the stage this morning, there's the difference between simple and smart. And often, smart will end up being easier than doing the simple. All right, Chris, really appreciate you helping us. You get a flavor for the show at the beginning. We've got lots more interviews to dig through all the product announcements, talk to the customers, talk to the partners. For Keith Townsend, I'm Stu Miniman. Back with lots more coverage. Thanks for watching the Q.


We were looking at the Kapitza pendulum where we had introduced a modification to the simple pendulum. The point at which the pendulum is suspended was being oscillated vertically in the same direction as acceleration due to gravity with a frequency capital omega and an amplitude small a. So, we had analyzed this system and we had written down an equation of motion for the same. In particular we had found that the equation of this pendulum actually behaves as if gravity becomes a function of time an oscillatory function of time and the effective gravity G prime is a difference between two terms the gravity if the pendulum was not in motion and then an additional quantity a omega square cos capital omega into t. Now, our task is to analyze this equation. So, as a first step let us write down the fixed points of this ordinary differential equation. Notice that this is a non-linear ordinary differential equation when we switch off the oscillatory motion of the point of suspension then it reduces to that of the simple pendulum. So, this is a non-linear ordinary differential equation let us write down its fixed points. So, as usual we define we write it as a as two first order ordinary differential equations and so we define the angle psi as x and the angular velocity psi dot d psi by dt as y. And then in terms of these variables by definition x dot is equal to y and y dot is just the equation of motion which in this case is I am shifting everything to the right hand side. So, this is G plus omega omega square A cos omega t sin x. As I had mentioned earlier you can readily see that the fixed points of the system in this case the fixed points are nothing but the equilibrium states. The equilibrium states are exactly the same as that of a regular pendulum that we had studied earlier. So, you can see that x is equal to 0, y is equal to 0 causes the right hand side of those two first order ordinary differential equations to vanish. Similarly, x is equal to pi, y is equal to 0 is another fixed point of the system. The main difference is that the right hand side is a function of time. In our earlier case this additional term was not there and so the right hand side was not a function of time. You can readily see that in this condition in this fixed point the pendulum is either vertically upwards or vertically downwards and you can think of it as if the effective gravity becomes an oscillatory function of time. So, these are these fixed points represent fixed points where the base state or the equilibrium state is actually time dependent. The tension in the string of the pendulum would have to instantaneously adjust to balance gravity if you are in the oscillating frame of reference. So, now let us analyze the motion of this pendulum by looking at one of the fixed points. So, let us look at the fixed point which is below so that is represented by this so lower point. So, this is theta is equal to or psi is equal to 0. So, this is the fixed point. So, if you leave the pendulum at theta equal to 0 with or psi is equal to 0 with 0 velocity the pendulum will stay there even though the point of suspension is moving vertically up and down with a certain frequency and amplitude. So, now let us substitute in this equations and so what we will do is we will we will perturb about the fixed point. So, we will say that the angle psi is so we are taking these two fixed points. So, the angle psi is sum 0 plus sum theta. Now recall that our original equation was that our original equation was d square psi by dt square plus 1 by l g plus a omega square cos omega t into sin psi is equal to 0. And if I substitute psi is equal to 0 plus theta then it just becomes d square theta by dt square plus 1 by l this part remains the same and then I have sin 0 plus theta. If I express that in a Taylor series about the point 0 then this just becomes the first term in the Taylor series approximation is just theta. Now this is an important equation notice that our original differential equation which was derived was a non-linear equation. We have linearized it about one of the fixed points. So, this is the lower fixed point about which we have linearized this equation or in other words we are giving the pendulum we are introducing the pendulum at its fixed point which is the lower most point the point of suspension is going up and down at a certain frequency omega and amplitude small a. And then we give it a small perturbation which is this theta and we ask what is the equation which governs theta if we retain only terms which are linear in theta in the resulting expression. So, we have to linearize this. So, if I linearize then I only retain the first term in the Taylor series expansion of sin theta about theta equal to 0 and so this is the linearized this is a linear equation. Now this equation the first thing to notice is that that this equation unlike the previous pendulum equation that we had the linearized pendulum equation is an equation whose coefficient is time periodic. You can recover the original linearized pendulum equation by just setting small a equal to 0. But notice that that equation we could have solved it by the method of normal modes. This equation has time periodic or time dependent coefficients in general this is the time periodic part and so this we cannot do normal modes on this. We cannot just say that theta is equal to some constant into e to the power some lambda into t this is that that form is not going to work here although this is a linear equation. So, this equation is a very well known equation it is called the Mathieu equation again named after the French mathematician who studied it. It frequently shows up in when we analyze stability of time dependent base states here as I told earlier the base state is time dependent. So, when we are perturbing about that base state. So, this is the lower fixed point is the base state here. So, the lower when we are perturbing about it the resultant linearized perturbation is governed by the Mathieu equation and since this is not a constant coefficient equation the coefficient actually depends on time and particularly they are time periodic. So, the solutions of this require some more effort than what we have done until now. In particular we will learn something called Floquet theory which helps us analyze these kind of systems. So, now let us start with Floquet theory. Now before we get into Floquet theory we will have to do a little bit of linear algebra while doing Floquet theory. So, I would request all of you to brush up your linear algebra fundamentals before going through this part. Now what does Floquet theory do? Floquet theory helps us in understanding the solutions to equations whose coefficients are time periodic. Recall that we have a second order equation whose coefficient is time periodic we have a cos omega t in the equation that I just showed you the Mathieu equation. So, I can use Floquet theory to analyze the equation because the coefficient of the Mathieu equation is also time periodic. Now, while drawing phase portraits I have told you that we can express any nth order differential equation as a set of n first order ordinary differential equations. So, it is enough to understand how does Floquet theory deal with a set of first order coupled ordinary differential equations. So, for that let us write down. So, what I am going to do is mostly going to apply to first order ordinary differential equations, but we have to understand that we can convert a second order namely the Mathieu equation into this form. So, let us first write down some of the things. So, we want to understand the solution to this first order system. Here a is a n by n matrix and x which I am representing as a vector is actually a in matrix notation it will be represented by a column matrix. So, it is a n by 1 n rows into one column matrix. Now, we have seen we know how to solve this when a is not a function of time when the matrix a is a constant matrix. We now we will learn how does that method extend when a becomes a time periodic matrix. So, now let us introduce some fundamental notation. So, in general this is a linear system this is a linear first order system because a is a n by n matrix I expect n linearly independent solutions. So, let us call those linearly independent solutions as so, let phi 1 of t phi 2 of t phi n of t be the linearly independent solutions to this system. So, now we will introduce a matrix which is called a fundamental matrix of the system and the fundamental matrix is obtained simply by writing all the linearly independent solutions phi 1 phi 2 these are all functions of time side by side in the matrix. So, each of them is a column. So, the first column of this matrix is the first linearly independent solution the second column is phi 2 the third column is phi 3 and so on each of them I will write as columns and because there are n n of them I will get n rows. So, I will get n columns and because each solution has n elements in it. So, I will get n rows. So, I will get a n by n matrix. So, this represents a n by n matrix now of what use is a fundamental matrix the fundamental matrix satisfies the equation. So, if I call this fundamental matrix as let us say I will call this matrix as phi. So, then the fundamental matrix satisfies the equation d phi by dt is equal to a which is itself a n by n matrix dotted with phi one can easily check this. So, let us take an example. So, suppose I have this set of equations. So, these are my coupled set of linear ordinary differential equations and I can readily see that I can the a matrix here is time dependent. So, if you collect the coefficients of x 1 and x 2 in both the equations and put them in a matrix you can see that they are time dependent because of this term and because of that term. So, now let us we can solve this set of equations easily these are coupled linear ordinary differential equations with time dependent coefficients this particular case can be solved simply. So, one solution is 2 e to the power t. So, you can check that this solution satisfies the equations similarly another solution linearly independent solution e to the power minus t 1 you can think a little bit about how did we obtain this solutions if you think a little bit it will become clear to you how does one obtain these solutions. So, these two are my phi 1 and phi 2 by previous notation. So, how do we set up the fundamental matrix? The fundamental matrix is phi and phi is just phi 1 and phi 2 written side by side. So, phi 1 is 2 e to the power t and phi 2 is e to the power minus t 1 and so there we have our fundamental matrix. Now you can immediately so the fundamental matrix is also function of time and now you can readily see that d by dt of this satisfies our original matrix would be the matrix on the right hand side a of t for this case would be 1 minus 2 e to the power minus t e to the power t minus 1 you can check that this is true just multiply the two matrices and you will find that the product of these two matrices will give you a square matrix. So, for example, and so if you take the differentiation of each of those terms you will see that I get that matrix. So, now we have checked that the fundamental matrix we have verified that in our example the fundamental matrix satisfies the equation that I have written this is the equation. Now let us use these ideas to go over to Floquet theorem. Now before we go to Floquet theorem it is important to realize the following thing that a differential equation with periodic coefficients need not have solutions which are themselves periodic in time. So, I will repeat that a differential equation with periodic coefficients time periodic coefficients need not have solutions which are periodic in time. Let us look at an example. So, I will take a simple example dx by dt is equal to 1 plus sin t into x you can clearly see that this is a periodic function it is a time dependent coefficient and it is a periodic function. So, this is a differential equation with time periodic coefficients can be easily integrated and the solution is x is equal to c 0 e to the power t minus cos t and if I choose x of 0 is equal to 1. So, then we get so this is 1 this is c 0 e to the power 0 minus 1. So, this is c 0 by e is equal to 1 this implies c 0 is equal to e. So, therefore, x is equal to e e to the power t minus cos t and so you can write this as e to the power t minus cos t plus 1 and you can readily see that this is not a time periodic function. In fact, you can see that if I write this as e to the power 1 minus cos t into e to the power t that part diverges in time alright. So, now we have seen that the solutions of systems whose coefficients are time periodic need not themselves be periodic with that background we will now move over to Floke's theorem. So, Floke's theorem says the system dx by dt is equal to the matrix a of t into x where a of t is a n by n matrix with period t has at least one non-trivial solution. I will call the solution as a column vector. So, it is a I am indicating it with a vector symbol chi of t and chi of t satisfies this relation that chi of t plus the time period of the matrix t is equal to some constant mu into chi of t this is Floke's theorem. It is useful and interesting to look at the proof of this theorem because it will tell us about the proof of this theorem contains some details but those details are useful when we later look at the Matthew equation and applies Floke's theorem on the Matthew equation. Recall that the Matthew equation is a second order equation with time periodic coefficients I can write it as a set of two first order equations. So, Floke's theorem will apply to the Matthew equation because the matrix a of t in the Matthew equation will also turn out to be a time periodic matrix. So, let us now go over to the proof of Floke's theorem. So, let phi be the fundamental matrix of the system by the we have just seen that this implies that d by dt of phi is equal to a of t dotted with phi a is a matrix phi is also a matrix both are n cross n matrix in general and we note the following that suppose chi of t is a solution to d chi by dt is equal to a of t dotted with chi. This is nothing but this system is nothing but our system of equation that I have introduced earlier. So, I have introduced this system earlier on which I had written the Floke theorem. So, I said that chi is a solution. So, I have replaced x by chi and I have rewritten the same equation. So, chi must satisfy this equation. So, now note that if chi is a solution to this and we replace then chi of t plus t is also a solution to the same equation. How do we see that? We just replace t by t plus t in the equation which is satisfied by chi. So, you can see that because capital T is a constant. So, the differentiation with respect to small t when I replace small t by small t plus capital T the denominator remains the same. This actually becomes t plus t now and this matrix becomes t plus t and this chi also becomes t plus t. But we know I will work on the right hand side, but we know that the matrix is a time periodic matrix. So, A of t plus t is equal to A of t. So, I can replace this with this. If I replace chi of t plus t with some function g of t it is important to remember that chi is not necessarily periodic. I had told you earlier that the solution to a periodic set of equations need not be itself periodic. Chi is a solution to a system whose coefficient matrix is periodic, but chi itself need not be periodic. So, chi when you substitute in the argument of chi t plus capital T it did not come back to itself. So, in general I will indicate chi of t plus t with some different function. So, g of t. So, this implies dg by dt is equal to A t dotted with g and thus we find that if chi satisfies this equation then chi of t plus t which I have indicated with the symbol g of t also satisfies the same equation. So, we conclude that if chi of t is a solution then chi of t plus t is also a solution. This tells us that if we discover one solution to this set of equation then if I take that solution and replace the argument with argument plus the time period of the coefficient matrix then what I will get is one more solution. This is what it demonstrates.


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