In the previous lecture, we started discussing on the seismic inputs that is the inputs which are necessary for analyzing the structure for earthquakes. Now, there are various forms of seismic inputs and the one which is to be used depends upon the problem at hand. Out of the different inputs, the time history records are the most direct and the easy seismic inputs. There are 3 components of ground motions which can be given as an input to a structure. Apart from that, there is a torsional component of ground motion and a rotational component of ground motion which can be obtained from the ground motions measured in the 3 directions. The frequency contents of the ground motion is an extremely important thing in the earthquake literature. Looking at the frequency contents of the ground motion, one can understand the characteristics of the earthquake and can take a decision about what kind of structure with its dynamic properties should be designed. The frequency contents of ground motion is also very important for frequency domain analysis of structures for earthquake. The frequency contents are obtained using the Fourier synthesis technique that we described in the previous lecture. Using the FMT algorithm, these days the frequency contents can be very easily obtained and a Fourier spectrum can be constructed for given ground motion. When we looked at the power spectral density function of ground motion, the description of the power spectral density function of ground motion is required for the random vibration analysis of structures for earthquake forces. In fact, in that case, the ground motions are modeled as a stochastic process and the power spectral density function forms one of the important inputs for analyzing the structure or considering the earthquake as a random process. And we continued with this and seen the definition of power spectral density function assuming the ground motion to be a stationary ergodic process. From the power spectral density function of the ground motion, one can obtain the peak ground acceleration using the relationship that is shown over here, that is in the equation 2.19c and this requires the knowledge of the duration of the ground motion, the capital omega that is this symbol and lambda 0. Lambda 0 is the mean square value of the ground motion or in other words, it is the area under the power spectral density function curve and the capital omega is equal to the square root of the second moment of the power spectral density function and divided by the 0th moment or the mean square value of the ground motion and taking a square root of that. Now, once we have the peak ground acceleration that is the knowledge of the peak ground acceleration, then this can be utilized for analyzing the structure for different levels of the peak ground acceleration. The predominant frequency or the period is where the PSDF or Fourier spectrum peaks. Another input is needed for probabilistic dynamic analysis of spatially long structures that have multi support excitations if exact results. So, in order to take into account the effect of this phase lag, the cross power spectral density function or cross correlation function is inputted along with the power spectral density function of the ground motion. Now, this time lag or lack of correlation between excitation at different supports is represented generally by a coherence function and a cross power spectral density function. The cross power spectral density function between two excitation which is needed for the analysis of such structures is given by these two equations. That is if X1 and X2 are the two points, then we say that there exists a cross power spectral density function between the ground excitation at these two points and it is represented by SX1, SX2 and that can be written as SX1 to the power half that is the power spectral density function at point X1, SX2 to the power half that is the power spectral density function to the power half at point 2 and they are multiplied by a coherence function which is a function of X1, X2 and omega. In fact, this coherence function is the correlation represent the correlation between the two ground excitations at points X1 and X2. For the case of a ground motion which is moving in a particular direction and if we the points are aligned in that, then the power spectral density function at X1 and power spectral density function at X2 they are the same or in other words in the sense of mean square value these two ground excitations are the same. And therefore, this product turns out to be the same as SX that is the unique value of the power spectral density function of the ground motion and it gets multiplied by this coherence function. Coherence function generally is a exponentially decaying function with the distance r and the value omega the greater the distance between the two points we expect that there will be less correlation between the two ground motion and therefore, a function is chosen which is exponentially decaying. So, this kind of function is multiplied with SX to get a cross power spectral density function which represent the correlation between the two ground motion in frequency domain. For a very small value of the distance between X1 and X2 and for small value of frequency we can see that the coherence function approaches towards unity that is we get a case of perfect correlation in that case the cross power spectral density function between the two points become same as the power spectral density function of the ground motion. Now, more discussion on the cross power spectral density function will be taken up in chapter 4 which we will discuss later. Then another interesting thing was observed for the ground motion although we have assumed that the ground motion is a stationary random process in which the mean square value along the ensemble does not change with time or is invariant with time, but in reality it is not so. It is found that the mean square value does change with time and therefore, we have to account for this particular pattern of the ground motion in modeling the ground motion as a random process. So, this is usually done by considering the earthquake to be a evolutionary stationary process meaning that the mean square value of the process changes with time in a particular fashion and the way it changes is a function called the modulating function modulating function which modulates the stationary process with time that is the mean square value changing with time. One such modulating function is shown in this figure later on we will see at the end of this lecture series on inputs that we have several empirical relationship or empirical equations representing different types of modulating function that are used in modeling the earthquake as a evolutionary stationary process. In the case where we consider the earthquake as a evolutionary stationary process the equation 2.2 to represents the evolutionary power spectral density function of the ground motion. Here the parameter t comes into picture because the power spectral density function changes with time and we obtain it by simply multiplying the modulating function square with the power spectral density function which we obtain assuming the earthquake to be a stationary random process. So, in order to describe the evolutionary power spectral density function of ground motion we must know the modulating function as well as the power spectral density function of the ground motion. So, these 2 inputs are provided for analyzing the structure. Now, from the collection of records various predictive relationships for cross power spectral density function Fourier spectrum modulating functions have been derived and they are given later or rather at the end of this lecture series on seismic input. Now, let us come to the next seismic input which is the most favored seismic input for earthquake engineers and this input has been codified and people use for the seismic design of structures for the design response spectrum and the basis of the response spectrum and the design response spectrum are the subject of discussion here. Response spectrum of earthquake is most favored seismic input for earthquake engineers there are a number of response spectra used to define ground motion displacement, pseudo velocity, absolute acceleration and energy. So, one can obtain the response spectrum for each one of these parameter the spectra show the frequency contents of ground motion, but not directly as Fourier spectrum does. Displacement spectrum out of them forms the basis for deriving other spectrum. The displacement response spectrum is defined as the plot of maximum displacement of an SDF system to a particular earthquake as a function of the frequency and damping ratio. I assume that all of you have a preliminary knowledge about structural dynamics there you have solved a single degree freedom system having a natural Fourier and a damping ratio to support excitation and for that support excitation you can obtain the relative displacement of the ground motion and that can be obtained by various method. For example, one of the method that is widely used specially in earthquake engineering to obtain the response of the single degree freedom system to a support excitation is using the Duhamel integral. This is the Duhamel integral which is shown in equation 2.23 where we obtain the relative displacement of ground motion using the recorded ground acceleration and using this equation. Now we can see that this equation contains a term which is some sin omega d t minus tau and other term is a exponentially decaying function which gets multiplied with this. The basis of the Duhamel integral I just want to mention so that you can recall it that if we give an impulse of x double dot g tau into d tau then the response at a time t will be equal to the free vibration that takes place due to the impulse. The impulse in fact provides a initial condition to the single degree of freedom system that initial condition is that the system is at zero displacement at that point if we assume but there is some velocity which is imparted at that particular point of time because of the impulse. Then for the elapsed time that is t minus tau elapsed time the single degree of freedom system vibrates as a free vibration problem or vibrates as a damped free system. Now using that concept we are able to obtain the x t using this integration. The maximum value of the displacement we can call it as S d is written as S v a parameter divided by omega n it results from this equation where S v is nothing but this equation that is this integration and the maximum value of that. That means we perform this integration at every time t and take a maximum value of that that constitute the value of S v and that S v divided by omega n and from that we get the value of the maximum displacement. Now this maximum displacement for different values of omega can be plotted for a given damping ratio. At the maximum value of displacement all of us know that the kinetic energy would be equal to zero because the maximum displacement condition is equivalent to the zero velocity condition and therefore the entire energy is the static energy that is half into k into S d square S d is the maximum displacement. So the other part of the energy that is the kinetic energy that turns out to be zero at the position of the maximum displacement. Now if we say that we want to express this energy as an equivalent velocity of the system then the equivalent velocity for the system can be obtained by equating this energy with half m v square where m v is the equivalent velocity square and from this one can get an expression for the equivalent velocity which is equal to omega n times S d that is the frequency of the oscillator multiplied by maximum displacement. Now if we look at the previous relationship that we have written X m to be is equal to S v by omega n then we see that the this X dot equivalent is nothing but S v itself. So we can write down X dot equivalent is equal to S v this velocity is called pseudo velocity and is different from the actual maximum velocity. The plots of the S d that is the maximum displacement and the S v that is the pseudo velocity over the full range of frequency and a damping ratio are called the displacement and pseudo velocity response spectrum. A closely related spectrum called pseudo acceleration spectrum also called spectral acceleration is defined as S a equal to omega n square S d. Now one can see that the omega n multiplied by S d that is called the S v and if it is further multiplied by omega n that is then we get the definition of the spectral acceleration. Now the spectral acceleration is the most important quantity in determining the maximum force that comes on to the structure during earthquake and the definition of spectral acceleration is consistent with that. So one can plot now the S a versus omega n for given damping ratio. So we can have we can plot 3 response spectrum that is the displacement response spectrum, velocity response spectrum and the spectral acceleration response spectrum or called spectral acceleration for different values omega n. In fact for the plots that are available they are the omega it is not plotted against omega n but they are plotted against the time period that is 2 pi by omega n giving the value of T n. So the plots are available against the period T n. Now if you look at the definition of the maximum force developed in the spring then one can show that the maximum force in the spring is equal to mass times the spectral acceleration that is obtained. Now this can be proved in this particular fashion that is k by m is equal to omega n square that is known to everyone then k becomes equal to m into omega n square. Now f max that is the maximum force in the spring that will be given by the spring constant k multiplied by S d and if we substitute for k over here that is m omega n square into S d that becomes the value of the maximum force. Now omega n square multiplied by S d that is nothing but the spectral acceleration S a that we had seen here from this equation S a is nothing but omega n square into S d. So therefore the f max becomes equal to mass times the spectral acceleration. Now that is a very interesting thing and the spectral acceleration therefore had become a very useful quantity for defining the maximum force in the structure. What we need to know for finding out the maximum force in the structure developed due to earthquake is the quantity mass of the structure which are easier to obtain than the stiffness. Now this observation shows the importance of the spectral acceleration. While displacement response spectrum is the plot of maximum displacement plots of pseudo velocity and acceleration spectrums are not so that is the pseudo velocity is not equal to the maximum velocity. The pseudo acceleration or spectral acceleration is also not the maximum relative acceleration. These three response spectra provide directly some physically meaningful quantities namely displacement response spectrum provides the information about the maximum deformation that takes place in the single degree freedom system. Pseudo velocity spectrum provides the peak value of strain energy in the system and pseudo velocity or pseudo acceleration spectrum provides the peak force in the system. Now let us come to energy spectrum. Energy spectrum is the plot of the energy of the system over a full range of frequency for a specified damping ratio. So the energy is expressed in this particular fashion that is written as square root of 2 times E t divided by m and the maximum value of this is obtained at every instant of time t. For example, if you look at the definition of energy at any time t, this is equal to half into k x t square plus half into m x dot t square and this dividing the entire thing by m and taking these two onto this side then we can write down twice E t divided by m is equal to omega n square k by m will be equal to omega n square into x t square plus x dot t square. So therefore, for a given single degree freedom system at every instant of time t, if we know the displacement and the velocity then easily we can obtain this quantity twice E t by m and the square root of that is obtained for every instant of time t and the maximum value of that is obtained and that maximum value is plotted against omega n and for a given damping ratio psi. The plot in fact also can be obtained for the time period rather than omega n. Now, for the damping ratio to be 0, it can be easily shown that the value of this maximum or this quantity root over twice E t by m turns out to be of this form and if we compare this equation with the amplitude of the earthquake amplitude or Fourier amplitude of the earthquake record then we can see that there is a similarity between this equation and the equation that is given over here. So, we generally say that the Fourier spectrum and the energy spectrum have similar form. However, Fourier amplitude spectrum may be viewed as a measure of the total energy at the end of t is equal to t of an undamped single degree of freedom system. Now, we take an example and draw the spectrums for the L centro acceleration for psi is equal to 0.05. Now, the equations that had been shown earlier using those equation one can obtain the values of S d, S v, S a and the maximum energy and can plot them against not omega n, but 2 pi by omega n that is the period for a damping ratio of 0.05 and these plots are shown in these figures this is the energy spectrum that is the maximum energy against the time period. That means, we change the oscillator time period every time we calculate the maximum value of the energy and that is how by varying the time period of the oscillator we can obtain the value different values of the maximum energy and plot them for a particular damping ratio. The same thing is done for the Fourier amplitude spectrum where the Fourier amplitude can be obtained against frequency or we can obtain also in the form of time period whereas, the response spectrum that is the acceleration response spectrum which is plotted over here that is plotted against time period. Now, if we compare the peaks of these energy spectrum Fourier spectrum and the acceleration spectrum the if these where the peaks occur if we find out then we see that the energy spectrum peaks around 0.55 second Fourier spectrum peaks around 0.58 second whereas, the acceleration spectrum peaks around 0.51 second that means, the ground motion has a predominant frequency content around a period of 0.5 to 0.6 within this range of the time period we get the maximum frequency content of the ground motion. Now we come to what is known as the DVA spectrum or the combined displacement velocity acceleration spectrums mind you displacement response spectrum is denotes the maximum displacement, but the velocity and acceleration spectrum are actually the pseudo velocity and pseudo acceleration spectrum they do not represent the maximum value of those quantities. Now, DVA spectrum forms the basis for defining the shape of the design spectrum that is used in different codes all over the world. Now, all the three spectrums are useful in defining the design response spectrum which we will discuss later a combined plot of the three spectrum is desirable and we constructed because of the relationship that exist between the three spectrums. For example, here we define the maximum displacement is equal to s v divided by omega n and therefore, by taking log we can write that log s d is equal to log s v minus log omega n s a the spectral acceleration can be written as omega n square into s d equal to omega n into s v. So, if we take a log of these then we get log s a is equal to log s v plus log omega n. Now, these two equations are shown over here and by looking at these two equation one can see there is these two equation represent two straight lines on a log paper and these two straight lines will be orthogonal to each other because one is minus other is plus and these two lines will be an inclined lines in a plot where log s v is the vertical axis and log of omega n will be the horizontal axis. So, taking advantage of these two relationship we are able to plot all the three quantities that is the s d s v and s a in a single plot being the logarithmic relationship or in other words a special kind of log or a graph in which we have four ordinates one is the horizontal axis in the log scale other is a vertical axis in the log scale and two other scales that is which will be inclined lines perpendicular to each other and also defined in a log scale. Now, these four axis define the quantities that is s v s d and s a for a given omega n value the plot also can be obtained not against omega n, but against t n that is the period in that case the two inclined lines will get interchanged that is the s a line would become the s d line and s d line will become s a line if we plot it against t n. Now, while plotting the response all the three response spectrum in this particular graph papers and which is known as a tripartite plot we need some limiting condition in order to define the spectrum. So, these limiting conditions are obtained by setting t tending to 0 in one case and in other case t tending to infinity and in fact it can be easily shown that limit of the maximum displacement as t tends to infinity becomes the maximum ground displacement itself. Similarly, the limit of the spectral acceleration as t tends to 0 becomes the maximum ground acceleration. Now, this can be easily realized from these two figures when t tends to infinity the frequency of the system becomes or tends to 0 and there those kinds of systems are called very flexible system. Once a system was shown for the earthquake measurement equipment that is there was a bracket and from that bracket a bob mass hangs with the help of a flexible stream and there was a drum and as the ground motion takes place in this direction then the bob goes on tracing the ground motion on this chart paper. It was possible because the flexible stream cannot pass on the vibration from this point to this point as a result of this the bob remains stationary whereas these entire bracket started moving like this. So, we can see that and that plot was this relative displacement plot came over here. Therefore, we can see that for a very flexible system the relative displacement of the system becomes equal to the ground displacement itself because the plot which you got is the plot of the ground displacement on the chart paper. On the other hand when t tends to 0 the frequency of the system tends to infinity or this is called what is as a rigid system the example of this is that we put a rigid block on a on the ground and if there is a ground acceleration here then the acceleration that is passed on to the top of the rigid block is the ground acceleration itself because the this entire rigid block moves along with the what you call the ground motion and there is no relative displacement of the rigid block with respect to the ground because it is very rigid and since there is no relative displacement and there is no relative acceleration and therefore the acceleration which is experienced at the top of the rigid block is the ground acceleration itself. So, therefore the following physical conditions emerge that is the limit t tending to infinity for SD becomes equal to UG max and limit t tending to 0 for SA becomes equal to the ground acceleration. So, now we show the plot this is the log SV that is the SV is in the log scale in the vertical axis and this is the log of not omega n but log of t n which is shown in the horizontal axis and this inclined line is one axis and this inclined line is another axis. Now, this axis corresponds to the acceleration in the logarithmic scale and this axis shows the displacement in the logarithmic scale again. Now, when we we can plot the SV versus t n in the logarithmic scale and if we make a plot let us say this plot looks like this for a particular ground record in this figure the ground record taken is the L centre earthquake and the dotted line is the averaged that means we have averaged that zigzag portion and more or less a smooth curve has been obtained for the L centre earthquake. Now, this plot which is the plot of log SV versus log t provides also the information about SA and SD that is if we measure that means if I take a point like this then for this particular point the SV value will be read from this axis SA value will be read from this axis and SD value will be read from a line parallel to this axis. So, any particular point reveals three quantities SA, SV and SD therefore, in one single plot we get all the three response spectrum. So, this is called the tripartite plot of the response spectrum in a special log graph paper. Now, what has been done is that the the graph that we get or that is a response spectrum that the smooth response spectrum that we get for a particular earthquake in this case is L centre earthquake this has been further idealized by a number of straight lines which are represented by the dotted lines over here and we obtain the response spectrum for a number of earthquakes and plotted them in the tripartite plot and those response spectrums show similar kind of trend and to understand that trend let us look at the different segments. For example, this is a segment which is designated by TA time period TA that is below this time period TA we have a segment then we define another time period TB between TA to TB we have another segment then from TB to TC we have got another segment then from TC to TD we have another segment and from TD to TE we have another segment and from TE to TF we have got another segment and beyond TF we have another segment. So, these segments are represented with the help of these time periods TA, TB, TC, TD, TE and TF. Now, if we plot a different earthquake spectrums in a tripartite plot and idealize them by straight line then we will get similar kind of form only the TA value, TB value, TC value these values will be different for different earthquakes. Now, each one of these segment represent certain thing that is what we are going to discuss now the straight lines below A and between points B and C are parallel to SD axis that is this line below A and between this point and this point if we look at these two lines these two lines are parallel that is what observe parallel to the line which is called the SD line. So, that is parallel to SD those below F and between D and D are parallel to SA axis that is this line and these two lines are parallel to the this acceleration or SA line below A shows constant value of SA which is equal to the ground acceleration and below F shows constant SD which is equal to the ground displacement that is what we discussed before that is in they give the limiting conditions that is here the limiting condition that value is shown as the acceleration that means the we measure along this axis therefore, it shows a constant acceleration and this shows a constant displacement which is equal to the ground displacement that is how the specified ground acceleration and specified ground displacement their maximum values are utilized in plotting this curve. In between these between B and C constants SA is equal to alpha times U double dot G max and between D to E that SD is equal to alpha D times U double dot or U G max that is this one this line and this line if we consider since this line and this line and parallel which is now logical is that these value that means this parallel line this will indicate a particular value of acceleration constant acceleration this constant acceleration will be equal to the constant acceleration or the ground acceleration that is shown over here the maximum ground acceleration which is which represent this constant portion this multiplied by some factor gives the constants acceleration over this inclined line. Similarly the maximum ground displacement which is represented by this segment and this portion of the segment which is parallel to this shows a displacement or maximum displacement which is equal to some multiplication factor multiplied by the maximum ground displacement. So, that is what is written over here the SA in that segment is equal to some multiplication factor alpha A into the maximum ground acceleration and on the other side the it is the maximum displacement is shown or the SD is shown as the some multiplication factor multiplied by the maximum ground acceleration. Now the left of C is directly related to maximum acceleration because in this plot we can see that on the left of C everything that is there that is parallel to the the SD axis representing the acceleration and beyond this point everything that is there that represent the displacement because there these lines are parallel to the acceleration axis representing the displacement. So the intermediate portion CD is directly related to maximum velocity of ground motion and most sensitive to damping ratio that is the horizontal portion it is obviously is most related to the velocity and this is also found to be very sensitive to the damping ratio that means if we change the damping constant we will find that in this range the response spectrum is varying widely. So, now let me summarize over here what we discussed. We discussed the cross power spectral density function that exists between two points along the direction of the wave propagation these cross power spectral density function represents the lag time lag or the lack of correlation between the ground motions at these two points and this cross power spectral density function is defined with the help of a coherence function which is exponentially dequeuing function of the distance between the two points and frequency. Then we obtained the then we started discussing on the response spectrum. So we have seen that there are three types of response spectrum acceleration response spectrum velocity response spectrum displacement response spectrum and also there is energy spectrum all of them can be plotted using a single degree freedom system and for a particular earthquake we can go on changing the period of the single degree freedom system and obtain these quantities and can plot it. Then we discussed about the DVS spectrum that is the tripartite plot where all the three spectrums can be plotted and can be seen with the help of one particular graph and the characteristics of the idealized DVS spectrum.


I want to show you my lunch every day, we are in a serious center. Because today is a Chinese New Year, so we have a special steam cake. You see, they open up. They open up, they mean fat go. Fat go, they mean get a lot of wealth, a lot of money. Fat go, they mean very good. And today is special also for Chinese New Year is roast pig. Chinese people always want roast pig for the special occasion. You see the skin, so crunchy, so yummy, so yummy. Everybody like the skin, roast pork, fish, chicken, barbecue roast pork.


So, any extra motivation tonight? Any extra motivation today? You were here last year? Yeah, of course. Anytime you plug into a former team. Let's see. Honestly, you want to win every game, but what is it that you do that plays the road to success? And do you think there's such and such long road? It's our offensive line. All credit goes to them guys.  And we just follow them behind us. They're getting us great holes to run through. So all the credit goes to the offensive line. You said, do I see us? Do I see us? Oh, sorry. It's kind of hard to hit with a mask. But yeah, my CS taking strides every day in practice. Coach challenged us. And we just try to make sure we go out here and execute. Yeah, I mean, it's important for us. I see us coming together as a team. We're a tight-knit group. And we just want to go out there and execute for each other. Besides Art cussing us out, I just want to say all offensive line, man. They've taken on a challenge. And they just want to prove to everybody that we can run the ball, those guys they can block. They did an awesome job against Tampa. And an awesome job against the Penns, I think. It's number one and number two teams as far as rushing. So like I said, we want to play for each other. We want to make the next play for the next man. We want to be able to count on each other. We hold each other accountable.  Yeah, the good thing about this team and our head coaches that he doesn't let up on us. He doesn't let us get down. And he makes sure we go out and execute. Make sure we know our team keys and make sure we know what exactly to do. So it all starts in practice. Rob, have you seen this? You said Mike Walker said that? No. But I was just happy for Mike Walker, man. I really appreciate him. He just had a baby. And so for him to come out and have a pick six, that's nothing but a blessing for him. And I'm thankful for him. Congratulations on your baby if you see this. But it's been a good week for him. Don't know how he came to practice the same day. But don't know how that went. But I'm happy for him. I honestly think you guys should ask him. I don't know if you guys have ever seen art on a sideline when we don't get a call. Like the two-point conversion, when Matt got his helmet almost snatched off. We didn't get a penalty. I think you guys should just pay more attention to Coach Art when things don't go right. There you go. Well, I guess he's a nice guy. Yeah, I mean, we talk about it, but we want to make sure that we focus on one game at a time. We know we have to do to moving forward, to get into the playoffs. So we're taking one game at a time and we know what our goal is. He shows us, honestly, our mistakes and how easily they can be changed. I mean, shows us what we can do better. And once we got that executed, how it looks. He makes sure, like I said, that we're not down. He keeps us upbeat. And he makes sure we know exactly what we have so everything in the game becomes easy. Yeah, I would say once he shows us these things and we're in a team setting and everybody sees it, and he tells us what you can do to eliminate it, I mean, guys never like to make the same mistake twice. So all our little things are easy to correct, like false starts and might point the wrong guy. So it's just something that we have to focus in on.


In this video, we're gonna do some soccer drills, some soccer dribbling drills. And I'm just gonna kind of freestyle this, show you a bunch of different drills that you can use to improve your skills. First one that we would do, and you've seen this before, it's these footwork drills. So this is dribbling, yes, but footwork, I think that's foundation. These little touches help you when you're doing more matrilistic touches. So start with the little stuff, the tops, I like these touches. These are some of the basics that I always do. The croquette attach, like an NES attach, the cuts. So whether that's one foot cuts, but also bending in these, getting lower the ground, both feet, changes of direction, okay? Then you can do those things moving. So if I just did the first touches, actually going places, whether that's front and back in different directions, okay? If you did that croquette attach, hooey, and if you make mistakes, just go again. But actually moving places with these touches, inside, outside cut. So those would be the first footwork drills that I would recommend. Moving into dribbling, actually with the head up, but changes of direction, something like that. So when you're changing direction, yes, you're focusing on the quality of the touch, but you're also focusing on the quality of the movement, the body control, okay? So when I make that touch, my upper body can't be here if I want to move, change direction efficiently. I want it to be down here because even if I have a bad touch, I'm on top of the ball, I can react quickly. If you're cutting your changing direction up here, slow, and if you do get a little bit of contact from a defender, he's going to push you off the ball. So whenever you're turning, changing direction, think about the sharpness of your touch, yes, but sharpness of your body movement as well. Next, you could do some 1v1 dribbling skills. So let's bring this guy out. Practicing attacking a defender. So first one might be something like that. These are all skills you've seen me do 100 times, but I like efficient skills that actually work. Okay, so when I'm doing these skills, again, the turn's still there, the forward's still there. Now we're incorporating and attacking someone. The timing of the move is extremely important. If I make my move too late, he's going to tackle me.  So over time, you're going to find the perfect distance to make this move at. With someone here, I want to force him to bite, force him to lunge for the ball, or force him to shift his body, his body control or his body positioning in one direction. If I want this space, if you like this content, check out the Soccer Success Planner. You can download it for free. There's a link in the description below. And for advanced training, check out the Online Soccer Academy. I want to push him that space. And if I want that space, I want to push him this space. Okay, so when you're practicing this, skills are great. But let's make it matrilistic. Because if you practice slow, you play slow. Yeah, it's good practicing my skills. But if I make my move and accelerate with that pace, I'm going to tackle it every time. So when you make your move, quick change of direction. Really focus on, after I make my move, this step here, try to get away from it a little bit. Because what's going to happen, if you're too slow, I might shift him. I might force him to go that way. Because I don't get away quickly, now I have to beat him again. Now I have to beat him again. And again, and I might have good skill, and I might beat him five times, but I haven't gone anywhere with the ball. So focus after you make that move, get away. Good. So I'm not big for cones, but if you like using cones, let's do a few cone drills. And now we'll breathe and recover in between. Talking and playing at the same time, makes for a good video content. Tough to do. Okay, cones are good for you to practice your technique. The only problem I have with cones is it's not match realistic. In a game, you're not going to dribble the same pattern 10 times in a row. But for foundational skills, young players, it's a good place to start. So what I love doing through the cones is the cuts. Okay, if you watch most players do this, especially young players, what is it? It's one, two, three. Are you seeing these little touches like this? Yeah, it's a good place to start, but it's not match realistic. In a match, you usually only have one touch to get away from the defender. And if you make a mistake like that, what do you do? You go again. If you're not making mistakes, that means the intensity of your training is not high enough. So you're not playing quickly enough or you're not forcing yourself to dribble when you're tired. You have to learn how to play when you're tired because when you're tired, the game does not stop. Okay, so cones, I think are really good for cuts, but is it match realistic?  So you can do this with cones. I like to do this with balls. So they're a little bigger, a little more of an obstacle to get around. But I might just set up some balls like this and then freestyle dribble. Don't stop the ball. Don't stop moving when you get tired, keep going. If you make a mistake, recover quickly, in and out. Be creative. Dribbling is also about creativity. If you're doing the same pattern every time, you're easy to defend. If you go the same way every time, you're easy to defend. Have some fun with it. If you like this content, check out the Soccer Success Planner. You can download it for free. There's a link in the description below. And for advanced training, check out the Online Soccer Academy.


Hi, I'm Zor. Welcome to Unizor Education. After we spend some time introducing the concept of a vector, well, let's try to analyze what exactly we can do with this, what its characteristics, etc. So today's lecture will be about one of two main characteristics of the vector. The main characteristics are magnitude and the direction. So today we'll talk about magnitude and considering that the vectors represent certain physical or geometrical quality of some object, we can talk about the lengths of the vector basically. So the magnitude as a philosophical concept is represented in the lengths of the vector. Now if vector is represented graphically like this particular arrowheaded segment, the lengths must be measured in certain units. So for instance this particular vector represents a speed. Well, speed can be measured in meters per second or miles per hour or whatever else. So somewhere we should have a unit of lengths which is equal to let's say one meter per second and then depending on the lengths in these units this geometric representation of the vector has certain lengths like 5.7 for instance. It means the speed is 5.7 meters per second. That's what exactly this represents. Now this is kind of trivial and easy. Now let's talk about the analytical representation of the vectors as as tuples as ordered set of numbers which are related to coordinate system. Let's say we are talking about two-dimensional vectors. So this vector has certain coordinates AB and the tuple A comma B represents the vector because it represents the endpoint of a segment which is originated at point zero zero obviously and so this particular segment represents both the magnitude which is represented in its lengths and direction which is represented basically by the direction from the point zero to point A comma B on the coordinate plane. Now considering we know only AB about this particular vector we don't have it visually, geometrically, we don't have anything. We still have to determine its lengths. Well but let's think about what is a coordinate system. Coordinate system is something which also has certain units of measurement on each on each axis. So the unit of measurement is given because the coordinate system is given. And what are these numbers A and B? Well these are the lengths of the projections of our point, the endpoint of the vector, to the corresponding axis which make up the coordinate axis. So this particular segment which is a projection onto the x axis is equal to three point something and this particular projection on the point on y axis is one point something. So what we know is maybe we don't know the lengths of this particular segment but we do know it's two projections on two orthogonal axes. Now obviously we should use the theory Pythagorean theorem to find the lengths, right? So this piece is equal to A, this piece is equal to B. So the lengths is equal to square root of A square plus B square. Because this is the importance and these are two categories. So what I want to do, what I want to actually say that this is the formula for the lengths, well this is a two-dimensional case. Well let's just spread it around. What if it's one-dimensional vector? Well one-dimensional vector is a vector which is represented on one particular single one-dimensional line and again there are units of measurements here and vector is again from zero to some point let's say to this point or to this point doesn't really matter. So in this in this particular case the coordinate itself but in this case it's 2.7. If the vector is directed towards the negative side it will be minus something. So what would be the lengths? Well the absolute value of this number, right? So in one-dimensional case length is equal to absolute value of the number which represents this is a one topo, so to speak, one-dimensional vector in its analytic representation. By the way these two formulas are not really different because you can always put it like this. This is the same thing, right? So if one coordinate, its square root of this one coordinate, if it's two coordinates it's square root of sum of two coordinates and now obviously we will go to three coordinates and you will see that things is very much similar. The vector in the three-dimensional space this is x, this is y, this is z. This is our point where the vector ends. Now this point can be projected onto the x, y plane. So if this is a, b, c then this will be a, this will be b and and this would be c. So imagine x, 0, y is a horizontal plane. Now the z-axis goes upwards so from this point I'm projecting to the x, y plane so this point is a projection of this point here. Now what's the coordinates of this point by the way? a, b, 0, right? And this height from the point itself to its projection on the x, y plane is actually the third coordinate. So this is c, this is the same length. So again this piece is equal to b, this piece is equal to a which is this one and this piece is equal to c. So what's the length of oa, oa. Now the projection is b and projection of b to these two are let's say c and g. Now oa is a hypotenuse of a triangle a, b, o. So a is above the plane, b is its projection so ob would be perpendicular to, so this is the right angle. So oa square is equal to ab square plus ob square. Now ob square, now this is the hypotenuse and this angle is the right angle, right? Because this is the projection onto this axis. So ab square plus instead of ob square, again Pythagorean theorem, I will use oc square plus bc square plus this. So this angle is right angle. If you look at this from the top, right? It's a projection which means we're directing the perpendicular. And now what is this? ab square is basically c square, the third coordinate. Now oc, oc is our a square and bc same as ob is b square. So again we look at this and we see exactly the same thing that the length of the vector is equal to square root of a square plus b square plus c square. So this is a typical situation with all the vectors regardless of the dimensionality. With one vector, with one tuple representing a one-dimensional vector, we had a square root of its one and only coordinate. In two cases, in two-dimensional case, the two tuple, ab. So the length is square root of a square plus b square. So again it's sum of squares of coordinates. And in three-dimensional case exactly the same thing. So basically using this, using this consideration, we can expand the definition of the length of the vector to any dimensionality. Now I mentioned to you that vector can for instance represent the oil refinery for instance, where all the parameters which are controlling the oil refineries are basically numerical components of this 100-dimensional tuple representing the state of the refinery. So the vector can be in 100 dimensions, right? So how to calculate the magnitude of this? Well, to tell you the truth, in case of oil refinery, it's very difficult to think about meaning of the vector, meaning of the length rather of the vector and direction. I mean this space is not uniform. I mean one component can be let's say a pressure and another a temperature. How can you combine together pressure and temperature? It's really hard to do. However, in some cases when components are not so drastically different, then we probably can't think about the meaning of the of the of the length of the vector. But in any case from the mathematical standpoint, which is a pure abstraction, we can always introduce something like this. So if vector has the components, we can always think about the lengths which is equal to the square root of some of their squares. So in this case it does make sense. So basically this is the definition of the lengths for all these strange situations. But in one, two, and three dimensions, it's quite an obvious thing that the formula is exactly what it is. And that's why it was expanded to other dimensions as well. Well, okay, so right now we basically know what the length is regardless of the way how we represent the vector. And we know about the geometric representation as just, you know, arrowheaded segment with a certain unit of measurement. You can just measure the lengths of the segment geometrically. Or in case it's represented as a tuple, then something like this would be the formula to to represent the the lengths of the vector, which means we know what is the magnitude of this particular vector. What is the magnitude of the of the certain physical or a real object this vector represents, whether it's a speed or a force or anything like this. This is the strength of the force or the real speed of the velocity, something like this. Okay, so this is a preliminary lecture about the lengths. Probably there are certain problems which I will think about and if I will come up with interesting problems I will just, you know, something in as a lecture. Meanwhile, you are obviously invited to take a look at the everything else whatever exists on Unisor, unisor.com and take a little bit more time to register to get engaged in enrollment in certain classes and then you will be able to take exams, which is very useful and you can take any number of exams and any number of times, each exam until you will reach the perfection. So thanks very much and good luck.


Hi everyone, Joe for jaspyscasebrakes.com, coming at you with the Jaspys eight box out of the park baseball mixer. Pick your team for the final version of this mixer. This was a good one. We'll have to think of another mixer now. We've got a wax party spot given away at the end, obviously all card chip. There's a few under wraps autographed baseballs in this break, by the way. So the baseball will go to the team they played for the longest if they're retired or their current team if they're active. Multi-sign auto baseballs will be randomized or given to a team at my discretion, at the breakers discretion. So let's just, before I show you the team list really quick, a lot of times it's gonna be pretty obvious. It'll be like the world series and it's all gonna be members of the same team. Right, that's probably members of the same team right there, right? If there's a, for active players, if there's like a specific stamp on there, what did I use last time? I used an example, yeah, like Bryce Harper. If it was like, if there's a all-star game stamp from a year when he was a national, it'll go to the nationals, obviously. If Splank just his autograph, it'll go to the Phillies. That's the team he's currently on. I think there's a, sometimes there's a case, maybe I'm making this up, I forget, but sometimes there'll be a dual auto, right? I think I saw a dual auto of some old school pitchers, like Steve Carlton and someone else. And they were once teammates, but they specifically inscribed their Sai young years, but they were different years when they were not teammates. So I ran a randomizer there. Now, if it didn't have those inscriptions, I would probably just give it to the teams. They both played on together. So they're pretty rare, but I just wanna put that out there. All right, so big thing. Multi-Sign autos usually have an extra authentication card and we can go there and try to gather as many names as possible or at least some of the key names and then we'll try to run a randomizer with that if necessary, but I think five stars, I think fanatics by the, not five star, I think fanatics is pretty good about making sure they're on the same team though. But those are my disclaimers. All right, here we go gang. Good luck. Thanks everyone for getting in. Eric M, last spot mojo brew crew. Some people winning their spots in the filler. However you got in, thank you, appreciate it. But yeah, some really nice products in this one. I agree, Eric, you soon. So we're gonna start with triple threads and we'll circle to five star, go back to the under wraps baseballs and then we'll play a little who am I. I'll give you some clues and you try to guess who the player is and then we'll end with that dynasty box. Was there an extra hidden here? I think so. And obviously all cards will ship. Corbin burns for the brewers. There's Devers to 259. That'll be for Ed P. Bregman to 299. That'll be for Percy and Houston. There's Mariners each year to 299. It'll be for David and the M's. There's the chip off the old blocks for Jones to 150 for Tristan and the ATL. A couple Yankees. All right, behind Stan, the man is a legend. It's Ichiro. Two color triple rally, 14 out of 27. And that is Mariners edition. David, I've heard of this guy. This guy's pretty good. Yeah, definitely LBC, beautiful cards indeed. And another Asian here, a Korean. We have a Japanese player, we've got a Korean player, Hyunjin Roo. 48 out of 75. My parents don't fall out of baseball, but they know this guy. Adam with Toronto. If this guy's healthy. He's never healthy, he's never healthy though. That was his knock with the Dodgers. And with the Blue Jays now. Behind Jose Ramirez, Bernie Williams. Two out of nine. Decade stats. Sordano and the Yankees. They got musicians in here now. I'm here all week, folks. He's a pretty good ball player too. We got Buster Posey, 47 out of 48. This Buster going to Chris and the Giants. My rivals, the Giants, but got to respect Buster Posey. Yeah, the golds do look nice this year, don't they?  It's a good idea. And the extra hit is a Yankee. Luis Evarino, 14 out of 18. Not a, it's extra relic there. It's for Dan and the Yankees. All right, one more triple threads. Let's get triple threads, triple threads. I want to get triple threads. Let's get into triple threads. Let me see your triple threads. Keep her on the website. Hopefully we'll have some more of this, more of this on order and on its way. All right, we got a redemption back there and another redemption over there. Yeah, that's the one like little thing, right? Where you wish more of these, if not all of these were on-car. It's already, it's a lot per box. It's a popular product, it's a lot per box. There's Trout for Dano. There's Mariano also for Dano. The big unit, Diamondbacks Edition for Preston and another one for Preston. They should try it one year. They should try just going all on-card autos, right? Jack up the price and then see if people will take to it because I mean, it's already really popular. Price goes up on it every year. Box price goes up on it every year. So all right, there's Southpaw, Slugger, Trevor Storty, 19 out of 36. That is Red Sox Edition, right? Yeah, Boston Edition for Ed P. And the other thing down here is Austin Riley, 30 out of 48. Also they kind of, it's not like that, but they kind of gave it a sort of pebbled design on the back, print on the back so it makes it look like it's textured, but it's not. But it's a nice touch. Nice subtle design touch there. Robin Yon's gonna help us out. Congrats to somebody you are due to receive a Triple Threads Autograph Single Jumbo Relic. Good luck. You should probably see the city first unless his name is long. B, not too many B teams. Baltimore, Boston. Oh, Boston. Jared Doran Doran. Save a prayer for me now. Save it till the morning after. Ed P. and the Red Sox. Everyone likes Doran Doran, right? Rock and Roll Hall of Famers. All right. You got it upside down, Rhino. Congrats. You are due to receive a Future Phenoms Autograph. Amethyst Parallel. T, Tampa, Texas, Toronto. Tampa, Tampa. Tampa W. Wander Franco.  Five star. We got the big dumper, Cal Raleigh. Rookie Otter for Seattle. That's for David. We got Smolty. John Smolts. That's for Tristan and the Braves. Not too many of these type of players, right? The starter turned, a star starter turned star closer. Could you almost say he was a better closer starter? He's a better starter. I don't know. He's pretty good at both. Accuracy, maybe? Is one other player starter closer? He was a pretty decent starter. Maybe not a star starter. Was he a star starter? I don't remember. Anyway, not too many players that can do that. I was just going to say, I don't know if I'm too much of a fan of his color commentary, though, on what, TBS, I think? We got Dylan Carlson. For the Cardinals. That's going to go to Ed P. It's St. Louis, St. Louis Cardinals. Another brave, Greg Maddox, 10 out of 25. Smolty, Greg Maddox for Tristan. Man, what if like Tom Glavin pop? Steve Avery? Slide Dynasty back there. We'll do that last. Put your thinking caps on. We'll do a few rounds of Who Am I? We have a black baseball with that gold trim. Gold stitching, nice. All right. I don't mind Oral as the color guy in the booth. He's a little homery, even for me, but it's the home broadcast. He's got a, you know, and he was employed by the Dodgers for so long and some of his best career moments were as a Dodger, so I get it. But yeah, he's all, I like him paired up with Joe Davis. You know who's great though? Dantro Willis. Dantro Willis is doing some color commentary for the Dodgers and for some national broadcast. I think he's a little raw, but I don't think he's done it too often before, but I think he's got a lot of potential. This one's going to be easy. A 25-year-old outfielder already with a 282 batting average, already 131 home runs. 323 runs batted in, 129 stolen bases. Already a three-time All-Star, an NL Rookie of the Year, two-time Silver Slugger Award, NL Stolen Base Leader, already part of the 30-30 club. Ridiculous. Yep, J-Loke 21's got it. Ronald Acunha Jr., not Juan Soto, although it's a good, not a bad guess either. There it is, on a black baseball gold stitching. That's pretty sweet. And you'll get the MLB hologram, and it's a fanatics product. You'll get their authentication as well. And obviously, place for the Braves. So that's going to go to Tristan and the Braves. A few Braves in a row, I dig that. Right, Tristan, yes, Tristan. All right, congrats, sir. I know, it's kind of weird.  No, Acunha, 18, 19, 20, 21, 22, and he was injured for like, so really, how many games has he acted, how many, with some couple injuries? Probably only three and a half seasons that he's put in the bigs. All right, is there any team identifier here? I don't think so, so this will go to the team he played for the long, because it's a retired pitcher. I'll take a closer look at it in a second. Retired pitcher, but a Hall of Famer, some great numbers. And I'm gonna, we're gonna use baseballreference.com. One of my favorite sites to see where he is. Play for 24 seasons. An MVP, a seven times Cy Young Award. You won seven times? A seven times Cy Young Award winner, won the triple crown twice, two World Series wins, seven ERA titles, All Star Game MVP, played for one, two, three, four teams, my entire career, ended up with a career, three 12 ERA, 354 wins, 4,672 strikeouts, a 1173 whip, not Nolan Ryan. Yeah, Nolan Ryan shockingly never won a Cy Young. This guy won seven. I've got a few kids in the big leagues too. Not Gaylord Perry, he wishes he had seven Cy Youngs. Randy Johnson, I don't think he even has seven Cy Youngs. Nolan Ryan has more strikeouts in this guy. Not Frank Viola, definitely wishes he had seven Cy Youngs. Wild Thing Vaughn, no, unfortunately, his career didn't last too long. He was a bright flame and then burned out. Not Cy Young himself, not Steve Carlton, CGK's guess before I even said stats was actually correct. James got it too, that's Roger Clemens. Rocket Roger Clemens on an old looking baseball here too. You got a Beckett card and you got the Fanatics card down there as well. And of course, Roger Clemens, the team he played for the longest was the Boston Red Sox, 13 seasons with the Red Sox. All right, so that's gonna go to Ed Pied, Boston. All right, there you go, Ed. You wish you'd be that easy, CJK, CGK. You know what, I haven't seen this guy's auto in a little bit. Another retired player. This guy's gotta be a future Hall of Famer, right? Catcher First Basement, one of those bats left throws right kind of guys. A one-time MVP, six-time All-Star, three-time Gold Glover, three-time batting title. I think mostly as a catcher. Five-time Silver Slugger. First round, first overall pick. Played for one team in my 15-year career. Put up some real nice numbers. Lifetime 306, 143 home runs, 2,123 hits. 923 RBIs, 52 stolen bases. A lifetime 827 OPS. Not Frank Robinson, not a catcher. Bill Mazurowski, also not a catcher. Not Ivan Rodriguez, not Buster Posey, not Jim Tomey. There's Chris Jaspy, I think he's gonna like this. That should give it away. Michael Singer and J-Loak21 got it. It's Joel and Joe Maurer with the beautiful hair. I feel like this is an auto you don't see too often. Not in group breaks. We've opened dozens of these baseballs too. I feel like I haven't seen a Joe Maurer auto. That's pretty nice. Got all the authentication right here. Hall of Famer, right? First foul of Hall of Famer? All right, and that's for the twins.  There you go, Walt. Nice. Two M's, and Walter's last name, yeah, two M's. All right, there you go, Walt. Thank you. Yeah, I always wonder if they should have moved him off of catching a little bit sooner to maybe, I mean, maybe he could have added another few more years to that career, but now it's still strong, still strong. Yeah, he did have that run before his MVP season. He was top five in MVP voting, even in the season after his MVP season, still top 10 in MVP voting. His MVP year just as a reminder, he hit 365 that year, led the league in that and on base percentage, slugging had, I don't even know how to say this, 1031 OPS, can you believe that? 1031 OPS, that's crazy. 28 homers out here, that's a career high. 96 RBIs, four stolen bases even. More walks than strikeouts, 76 walks, 63 strikeouts, 191 hits, 30 doubles and a triple. Why not? 94 runs scored. Looks like CGK lagging behind a little bit. Make sure you're watching live. Had a seven, eight war, which easily led the AL that year. Behind him Tashara, Jeter, Miggie, Miguel Cabrera, Kendris Morales finished fifth in MVP voting that year by the way. All right, final box, good luck everybody. Yeah, LBC got it in the Twitch stream too, Joe Maurer, he's pretty good, breaking news. All right, good luck everybody. What do we got here? Where's the name at? You'll see the team colors first. Is that Orioles or Giants? Orioles, four out of 10, Cal Ripken Jr. Nice, that's gonna go to Aaron who bought Baltimore straight up. Be more, nice, the Iron Man.  What a break, really nice stuff. Thanks everyone for joining. Now, let's see who's gonna get that wax party invite. Check out the details of that promo on jaspyscasebreaks.com. It's pretty, pretty, pretty good. Let's go back to this list right here. Let's get one through 30. Let's gather everybody's names and let's roll it and randomize it one out of five. Name on top, after six gets the invite. Good luck. One, two, three, four, five, and once more, six and final time. After six, there's gonna be a lot of sad faces here. Saddest of all, spot two. Close only counts in horseshoes and hand grenades. I think this might be the second time in a row. Or maybe the second time tonight where you've been second, sorry man. I appreciate you putting in the work though. Two through 30, thanks everybody. Appreciate you. There's a lot of invite opportunities at the moment. So if you feel like trying again, you know where to go, jaspyscasebreaks.com. All right, sorry guys, but congrats to Daniel. There you go, Dano. I don't know if I called your name out too often this break, but you're in the wax party. You're guaranteed something and check out the grand prize. That something could be a really nice something. I'm Joe for jaspyscasebreaks.com. Thanks for watching. I'll see you next time for the next one. Bye-bye.