all right hello and welcome to the second lecture for chapter six chapter six from physics of everyday phenomenon griffith first author and what is chapter six all about it's about introducing energy in the first lecture we covered just section 6.1 but it was about half the slides in our lecture slides from the publisher and well we introduced work we related work to force we talked about work being a scalar we saw a formula for work okay but now excuse me we are ready to move on okay so the first kind of official form of energy because people sometimes separate the concept of work from energy okay they both have units of joules they're interchangeable it's just how you calculate them because work is a usually a constant force over a well-known distance and it has that formula work equals force times distance that's a particular situation that's a particular system that leads to that type of calculation all right so many times we we're not going to focus on the work because it would be impractical to calculate it instead we can look at little snapshots in time calculate the sum of particular energies one of them being kinetic energy and that is the approach that's known as energy conservation because energy conservation is as much a law and it is it's the law of energy conservation law of energy conservation conservation excuse me as it is a tool okay because it really is a way to solve problems because you can track the energy and solve problems that you otherwise couldn't solve okay so our first moving on from work our first form of energy that we are analyzing known as kinetic energy is the energy associated with motion okay you don't have kinetic energy if you don't have velocity objects at rest have zero kinetic energy okay now doing work on an object increases its kinetic energy but not just work from a single force but doing a non-zero network okay if you have two forces that do an equal amount of work but one of them is friction doing negative work and the other is say a pushing force like this one doing positive work well the net work would be the sum of those two identical identical magnitude values of work but since one is negative and one is positive your net work is zero so in that case your kinetic energy would not change you'd have some kinetic energy but you would just be moving at a constant rate therefore there'd be no change in kinetic energy so the net work done when it's not zero is equal to the change in kinetic energy those would be cases like you're pushing hard enough on the crate crate to overcome the force of friction and then some so as you push on the crate it actually is speeding up as it goes so this is exactly what's shown in the picture here because we see that the crate large box here with mass m started with velocity zero okay so it started from rest after covering some distance d it actually is moving at a velocity v so it clearly accelerated which means that the that the net work had to be greater than zero because the change in kinetic energy was well not zero okay and the form of kinetic energy is one half the mass times the square of velocity this has the same units as work this is also newton meters but we would never express it that way we always express the units of kinetic energy in joules which we sometimes express work in okay so we talked about negative work i talked about it before i taught even gay we saw a numerical example at the very end of the last last lecture video but let's cover it again to relate it to kinetic energy so negative work is the work done by a force acting in a direction opposite to the object's motion okay it's still parallel in the sense that the work isn't zero but it picks up a negative okay so for example a car skidding to a stop well the force that slows it down is the force of friction we're gonna assume that's the only force because the car is completely stopped accelerating right you know generating thrust so it's just the force of friction slowing it down and then it that force of friction is going to slow it down over some total distance okay and then it's going to finish with a velocity of zero okay so that's the force is the force of friction and there's a key set of formulas right down here where we can actually see that the work is equal to the negative times the mag the magnitude of the force of friction times the distance right which is always going to be positive right so it's going to be negative work and that's going to equal the change in kinetic energy so that means that the kinetic energy had to have a negative change how's that well think about it the final kinetic energy is zero the initial kinetic energy is something other than zero would be one half mv squared mass of the car one half and whatever its initial velocity is when it started to break okay so you have a difference that is negative the kinetic energy went down it decreased to zero so work is done but no kinetic energy is gained okay then what happened right then something else had to change now one case is that all that work that's being done that isn't changing the kinetic energy is then just being turned into heat in that case there actually is no gain in potential energy we'll come back to that concept and mention how friction removes mechanical energy okay so the same friction that we're talking about here removes mechanical energy in this case the only work being done is is being done by the work of friction right and you know and what's happening right the the kinetic energy is changing right in the negative direction sure but it is changing right and is there any gain and potential no right absolutely not okay so this is a case where we have no gain in potential energy and where the where the energy is going where the the loss of kinetic energy is ultimately being tracked because conservation of energy is all about tracking things is it's going to heat because that's precisely what friction does fiction removes mechanical energy from a system kinetic energy is an example of mechanical energy i talked extensively about mechanical energy in the last video so then we have a case where we're removing that so in that sense and this is what friction is often classified as friction is a non-conservative force because it doesn't conserve mechanical energy but don't get me wrong friction conserves energy but in a broader sense than mechanical energy because heat is not mechanical energy okay heat is another form of energy among quite a few right a list that isn't infinitely long but has quite a few different types of energy you can gain okay we're focusing on the basics and getting back to the basics a form of potential energy that you can easily gain with it kind of a simple experiment a simple machine because we got a pulley here bring it back to the very beginning of this chapter okay in the beginning of the last lecture video well when you have a simple machine like this and you are exerting a force on the crate right so you're pulling you're pulling the crate up well then what what's happening right what what is the result of the work that you're doing on the crate well the crate is gaining gravitational potential energy okay you right up here right pulled on the crate you did work on the crate so we would say that work was done on the crate by an external force that work being done on the crate resulted in a change in gravitational potential energy now could it have also resulted in a change of kinetic energy sure that'd be a case where you lifted the crate and sped up the movement of the crate and honestly of course there would be some movement usually in this case though the crate may be you know started on the floor at rest and once it's lifted up to some final height it's going to then meet maybe dangling at rest and even though there was changes of kinetic energy throughout that motion we're just going to look at the beginning state at rest and the end state at rest and that's enough for us to say well then that case will all the work that was done ended up just resulting in this increase in gravitational potential energy okay ignoring things like friction and air resistance right maybe friction in the pulley so why why is that like such a good example because as i was saying it you know saying you know look at the beginning point look at the end point i feel like that's such a just perfect example of what energy conservation is all about because energy conservation is all about comparing between two points it's not about the process in between many of the forces that we actually discuss are forces like gravity even the electrostatic force in later chapters and those forces are path independent it doesn't matter how you know how you got from one point to another it only matters that you decreased in gravitational potential energy okay in terms of tracking the energy and seeing you know where it went now there's some things that are path dependent like friction so if you take a longer path obviously you have more time to interact you know and lose energy to heat so it all depends how you how realistic you want the system needs to be right does it need to consider things like you know friction forces and drag forces or not right because obviously we're not we're not considering that here right here we're just saying that all the work that's being done changes the gravitational potential energy an ideal consideration okay so the work done is equal to the force mg okay so that's just gravitational force think newton's laws times the distance because that's that's the definition of work force times distance in this case the force and the displacement are parallel to each other so no negative okay so then the work done is precisely mgh well if the work done entirely becomes gravitational potential energy because it does 100 percent okay in an ideal system that means that the gravitational potential energy is exactly mgh all right now this isn't in a big box like the last one but it kind of could be right so in fact let's jump over here real fast and we'll go over to that side because in the same way i said the last one i was referring to the last named energy type kinetic energy because really this form of gravitational potential energy is very important and it has it absolutely has this you know um this um expression right this formula right i just got a fluster there because my pen is not responding trying to figure out why okay so let's see if i can yep i'll make it work with my finger all right bear with me so um so then we just have that the force excuse me the because we're talking about gravitational potential energy so we had ke for um kinetic energy so sticking with that same type of terminology we'd have pe okay so am i do i have anything working now no all right so let's go ahead and switch back for now and i'll be uh i'll be with you on that one get things uh get things fixed on my end all right so anyway that form which i will show you as a formula when i do a numerical example at the end of this video so stay tuned um if you want to for a numerical example at the end of the video okay so potential energy is mgh okay so work is done on a large crate to tilt the crate so it is balanced on one edge rather than sitting squarely on the floor as it was at first has the potential energy of the crate increased right so we just pushed it up on its edge did we doing something like that right think about it because what is gravitational potential energy right did you do any work in this case right and then way i remember potential energy being explained to me when i was a physics student was that that potential energy has the potential of doing something okay i'll probably say that again because it has the potential of doing work right in this case we did work for the crate to gain the potential energy but now the crate itself can do work right if we release that potential energy okay it has the potential of turning into kinetic energy right so these so that that's that's what potential is all about okay so did you gain potential in this case absolutely okay because if you if you're thinking yes but you're not sure why the way that we officially describe this is because the center of the mass has gone up okay the center of mass would be you know if it was you know if this crate was uniformly distributed with its density would be right in the geometric center and we tilted it it actually raised a little bit okay you can of course show that geometrically and so on okay so the term potential energy implies storing energy right i knew it was coming and i'd seen that slide storing energy to use later for other purposes okay so excuse me there i am all right so storing potential energy to use later right such as right i don't know breaking a coconut right doing work in this case right um you know exerting um exerting a release of energy because you might say well the coconut kind of explodes how does that work well you know explosions are our energy and that's a that's a great versatility of tracking energy and considering conservation of energy because you can come up to systems that are a little messy and hard to quantify and say well you know but but maybe you could at least talk about the total energy released you know when the when the coconut you know exploded right well there you go that energy had to come somewhere it would have came from the release of gravitational potential energy okay dropping this crate now there's another type of potential energy in fact there's many but there's another type that's considered mechanical potential energy okay so that means there are two types of mechanical potential energy all right gravitational which is the more fundamental absolutely all the pulleys and lifting things and and gravity dominating our lives because we live on the surface of a planet you get it right but springs are a big deal too and the way they store energy is pretty evident right you can release the energy of a spring and it causes something to you know quickly accelerate gain kinetic energy you know and springs have you know tons of practical purposes and there's a great demonstration of kind of physically storing that energy okay now i went off on a small ranch in the previous video when i was talking about all forms of energy and how elastic potential energy okay elastic potential energy um is considered mechanical right so be introduced in a chapter like this but ultimately what makes a solid it's mostly actually electrostatic forces between molecules and atoms so you know it is what it is okay but still consider mechanical on the table top on the in the everyday case now what's interesting is that word elastic just means stretchable right now a metal spring is metal but metal is stretchable especially when it's you know wound up in the shape that makes it more easily deformed but in general metals are defined as quite elastic so they can experience some deformation and return almost exactly to the original shape they're actually more elastic by that definition of being able to return to their original shape than a rubber band right you think a rubber band is being really elastic but a rubber band is actually very ductile which means it can be stretched many times its original length but they're not that great at returning to their original shape they constantly lose their stretch right just after you know a few uses because they they just they start to degrade right metal doesn't have that so they follow that strict definition of being able to return over and over again so it's very a very good elastic system interesting right so just kind of our as our everyday understandings the understanding of what something elastic is versus you know versus what the you know the physics or engineering definition tells us now the way that we actually quantify springs is with the spring constant okay so wow we gotta wrap our heads around that where the heck is it okay it turns out it doesn't is gonna have units okay k absolutely has units it's not a dimensionless constant okay it's a value and what is it it's a proportionality really it's a ratio it tells you how much stretch you get for a certain amount of force okay and it works as long as your spring has a linear behavior between force and stretch so in other words if you pull twice as hard on the spring you get twice as much stretch you pull three times as hard you you got you change the length by three times as much as when you pull twice as hard right and so on so that's a direct one to one you know like it quadrupled to four you know you know five times to five and so on you know so that is a linear relationship and that's what you need to have this ideal spring now metal springs behave pretty well when i do a physical hands-on lab in the in the classroom you know in the laboratory classroom they we see that it really is linear okay that's called hooke's law that linear relationship works great for these metal springs okay interestingly if you just go and grab some sturdy uh rubber bands and do the same sort of experiment you'll see that it doesn't rubber bands are noticeably just that kind of the same range that you would test a metal spring not behaving linear okay they start to really show that that deformation and just different behavior at different stretches okay so okay we're gonna have a new form now for this type of potential energy elastic potential energy okay and it comes from a little argument about thinking about how how the force is being done okay so now i will go back over to the tablet so i can take a look at this okay because i want to highlight some things in this graph here because the vertical axis is kinetic energy okay it's not i saw the k and said kinetic energy but it's not at all the vertical axis is the spring constant times displacement so what is that well that is just force okay it's precisely force okay because hooke's law which is this law that applies to springs and says that springs behave in a linear way twice as much force twice as much stretching okay they just say that f right for the spring just equals k x okay so if i if i was to look at a graph and i was just to look at you know like how much you know what the um you know the force right like on the this exact graph in fact if i was to look at this graph right here right um and you know acknowledge that yeah sure force equals kx that's the formula that is literally hooke's law well that also tells me that if i have force on the vertical axis and i have displacement on the horizontal axis then i've got a graph in the form of you know y equals mx right no you know vertical intercept so no b because it goes right to the origin right so i just have a simple line here well m is the letter we typically typically typically use for the slope of a graph and this is just a mathematical formula these are not physical variables if you haven't seen this formula that then ignore it but if you have then you know that it's just a common way of expressing the equation of a line okay m is the slope okay so in that case what's the slope the slope is the spring constant okay so k is the slope it's that linear relationship some springs might you know have a steeper slope right steeper slope because they are stiffer right it takes more force to stretch than a certain amount a spring that has a less steep slope would be a spring that is not as stiff right it's easier to stretch it's a little bit kind of just you know like a ductile that term i said i used for rubber bands right but maybe in a more linear way okay all right so with that in mind just establishing you know how springs behave then we want to jump right into their energy because that's that's why we're looking at this that's what we care about is the energy okay so we've got that potential energy is work done okay that's always true so a gain in potential energy is always work equal to the net work done all right because it's got to be the total work usually we just consider one force so keep it simple but technically it's a network okay now that's also equal to the average force times distance why average force well because most of the time we've just said force because we assumed our force was unchanging well with the spring it's definitely not unchanging okay it changes clearly clear cut all right so this is a non-uniform force this is a force that itself is a function of the displacement this is the kind of thing that leads to this necessity of calculus this is what led to newton you know coining calculus creating calculus from scratch because he realized that you had to be able to solve problems like this and the math didn't exist okay and we still use that math today we still use calculus to deal with rates of change like this where you have you know one thing that you want to calculate that's dependent on the other thing that you that's related to it okay but in this case because it's linear we don't even need calculus we get the same result of calculus we can actually make a graphical argument and say well check it out right the area under the curve much must represent the energy right because what is what are the units of this shaded kind of orange tan color right well the units would be force right the vertical right the height times the base right the the width of it which is x right that's newtons times meters that's newton meters okay so newton meters it's joules okay so the shaded area is an energy okay and that shaded area being a triangle is just one half base times height okay one half the base times the height what do you get you get right one half kx squared because the height is kx as we were talking about because that's the force that's hooke's law all right okay the average force is one half kx which again is just the formula for a triangle right because literally right this is you know taking the average force and then multiplying it but that's that's how you do a triangle right so the area of a triangle is just one half base times height in this case your height is kx h is kx and your base is just x so when you multiply multiply that together all right well what do you get one half kx squared okay so this right here one of our three big types of energy is elastic potential energy i haven't put a couple letters down here to distinguish that we're talking about elastic potential energy and not confusing it with gravitational potential energy which for some reason just didn't get its own box but we'll fix that all right so giving the potential energy the big focus that it deserves and we'll shade it in so it looks like something like the other formulas okay so now in summary we've got our kinetic energy one half mv squared we've got our gravitational potential energy so g for gravitational and then we have our elastic potential energy right here okay now it's funny that elastic potential energy looks so much like kinetic energy with the one half and the squared right it's like you just replace the m with a k and replace the v with an x that's because it comes from the same sort of linear argument and considering the area under a triangle okay it comes from the same sort of mathematical considerations we're not going to show it show it this time but suffice to say it's quite a similar derivation okay so the big thing we do with this these concepts with these three types of energies is we look at systems that we that have a conservation of energy and how we can then move from one point one snapshot one instantaneous moment to another within that motion okay so let's consider then a conservative force that's like gravity okay or an elastic force and a conservative force right um are ones that can be completely recovered so gravity and elastic forces as i said friction is definitively not okay because once you turn energy into heat you can't just turn that heat energy back into other types of energy okay you can you turn some of it back sure you can build a heat engine okay as they're known but you can't turn it all back in fact that's its own law called the second law of thermodynamics which basically says you can't get 100 return you know from heat to mechanical energy so that's interesting right that's as part of kind of why it's called non-conservative it's also just called non-conservative because it's it's the idea that it's leaving the mechanical system okay but you can't get it back so that the idea then is that you could look at these snapshots right these moments in time when i present problems i will you know i will solve them by saying consider point one consider point two consider that the total mechanical energy of the system is conserved between points one and points two right because there's no friction in this idealized case or maybe there really is no friction maybe this is done in a on another planet where there's no atmosphere okay in that case g would be something else unless it was exactly an earth analog that had no no atmosphere right but then what you would say is you would send e one equals e2 okay so the total mechanical energy is conserved from one step to the other the total mechanical energy at point one is entirely potential energy okay so it's entirely just mgh and then on the other half the energy is just entirely one half kx okay excuse me mv squared okay so i had a few interruptions this video it's throwing me off okay but that's the idea is the mechanical energy went entirely from one form to another okay so that's the idea of conservation of energy okay is it always conserved yes is it always conserved as a mechanical energy no okay friction all right and as we'll see later as i said electricity magnetism okay so let's do a quick question here a lever is used to lift the rock will the work done by the person on the lever be greater than less than or equal to the work done by the lever on the rock okay so what do you think think about conservation here okay no friction by the way that's a hint right but you know this is a machine this is a force multiplier okay review the beginning of the last video if you want to if you don't know what i'm talking about so you got your answer locked in okay all right let's take a look then okay so we've got that it's c it's equal right even though you got more force on the way out right you put in a small amount of force and you got a big amount of force out that's the whole idea right get a really large force out you gave something up as i talked about before the whole way that the mach that this you know simple machine works is you have a relatively large displacement with a small force all right this is your initial displacement and then that's going to give you a quite small displacement over here all right so it's going to lift up here i'll show over here it's just gonna lift up a little bit okay it's gonna be much more even smaller area right so we're gonna have a little bit of lift well then what is you know what is force right what is work more importantly work is force times distance so you essentially had a big force small distance equaling a small force big distance but the energy is conserved because the work in equals the workout why because you can't create energy if it wasn't conserved where's the extra energy coming from right you didn't like you know release some chemical energy or something this is entirely mechanical all right so you then can have cases where you convert potential energy to kinetic energy other than pendulums because that's the one we saw over here right this one was a great example of the pendulum the pendulum is such a great iconic example of this process but there's more to it right we've got you know sliding a sled down a hill or a roller coaster is another iconic example of you know getting up to the top of the roller coaster you have a bunch of potential energy and then you can let that potential energy go and come down the roller coaster okay you did work to gain in the first place right in this case actually you know applying a force pulling up hill and it looks like you know if you pull directly parallel your displacement then you're all that force is doing work right but you're working against gravity okay you get to some height right then you release you release that um some of that potential energy see that can you call that your initial height right but then you get down to a point here that isn't zero right because you haven't done all the way down the hill the idea is you went you dipped down you got right back up to some rise right when you did that when you get to this point you have a mix of potential energy and kinetic energy because you don't have to have all of one or the other when i looked at when we looked at the pendulum and i you know i wrote the two points points one and two those were two carefully chosen points where the energy was entirely potential gravitational potential at the top and entirely kinetic at the bottom of the swing okay but you can absolutely have a mix of the two obviously any anything on the way okay right so any work however done by friction removes mechanical energy so whatever so if you were to if you were to calculate say the final kinetic energy by you know considering that all the gravitational potential energy transformed into kinetic energy and that's what we say we see the energy is transformed from one type to another well if you did that right and you were able and you say calculated the final velocity with that method and you ignored friction but there was a non-ignorable amount of friction well what would you be doing you would be overestimating the velocity because you'd be ignoring the energy that was lost to friction the energy that was removed from the mechanical system and turned to heat via friction okay now friction has that is a negative value of work which makes a lot of sense that negative fits really well with our conservation equations because we can we can literally say okay we have some energy here right energy at point one when the person was higher up the slope you know when they're down lower at the slope we'll call that energy at point two all right when we compare the energies and we we say that e the e letters here represent mechanical energy well then what we have is we have e1 plus the work done by friction equals e2 and you might be like wait why are you adding the work done by friction well because you know if you think about it you e1 was just how much energy you started with okay and then e2 is just how much energy you end with between these two points well the work of friction you know comes between them right so you have to add the work friction to the initial value but here's the thing when you add it what do you get you get a you know you get a negative right because you're adding something that is negative so for example this might be like mgh right if h was you know that the height to here okay and then that would be minus the force done by friction times d okay and then that would equal at point two if we say that's the bottom right that would equal entirely kinetic energy one half m v square okay now what's interesting is h and d are definitely not equal to each other all right and if this is like a nice like ramp then you could use trigonometry to relate h and d we would not in this class but you could but if it's like a slope like this then you you need to know d you have to actually go out there and measure it and that's why um friction becomes you know impractical to you know calculate at the same precision as gravitational potential and kinetic because finding d in practice is pretty difficult all right so let's do another question a sled and a writer with a total mass of 50 kilograms are perched at the top of the hill showing suppose that 2 000 joules of work is done against friction as the sled travels from the top okay the higher hump to the second hump at 30. all right will the sled make it to the top of the second hump if no kinetic energy is given to the sled at the start of its motion okay so think about how much potential energy it has how much it needs okay is is this value of friction is it so big right is it is it enough that it can't make it okay think think about your answers think about how you would actually calculate this make sure remember the gravitational potential energy potential energy is mgh that'll help give you the kind of values that you'll need to compare to 2000 rules okay and 2000 joules is shown as positive but then it's we're told that it is the work done against friction which means that friction is doing the negative 2000 right okay so ready to take a look at the answer actually let's go back over here for a second yes okay the difference between potential energy at the first point in the second plate point plus loss of friction is less than the potential energy at the start the sled will still have kinetic energy at the top of the second hump okay there's enough energy for it to not just get to the top but actually get there and keep moving right at some non-zero velocity okay so now we'll talk a tiny bit more about springs okay so the motion of springs and we talked about hooke's law and the fact that springs are defined by that one value the the spring constant well that results in a certain type of motion if you were to pull a spring back or rather a mass attached to a spring in this case we're assuming all the masses in the block the spring has none of it right the spring is ideal and massless okay but when you release the block you're going to release kinetic energy potential you know um see excuse me you're gonna release elastic potential energy that elastic potential energy then will transform entirely into kinetic energy at the equilibrium length of the spring okay so that's a that's kind of it's really analogous to the pendulum swinging down to the low point because this is the point where all the energy is connected okay for one one instant in time right after that however since the mass has inertia it will continue on its way and it's going to transform that kinetic energy back into potential energy yes compression of the spring but totally comparable elastic potential energy in fact exactly equal in magnitude so you're going to have this perfect exchange whatever you know maybe 10 joules of potential energy to start with all elastic gets transformed into 10 joules of kinetic energy right at equilibrium right at the x equals zero point okay also the natural length of the spring and then right back into 10 joules of elastic potential energy at full compression okay so and what's interesting is there's no negative potential energy here right at least not with the elastic case it's positive on both ends it's just oscillating back and forth between those two positive energies okay now the motion okay is similar to that oscillation the motion ends up being sinusoidal which is because what we're looking at here is we're looking at something that's a repeating process we represent repeating processes by something that's cyclical and circular and it's the same math that applies to this case of something bouncing back and forth it's got the exact right behavior and we can see that if we kind of take a look at this potential versus time graph in just a little bit more detail because remember what is the instantaneous tangent line the slope at any point on a position versus time graph its velocity right so if i look at the slope right here where the position passes through zero the equilibrium length of the spring you know the um the natural length of the spring that's the steepest the slope is going to be right so this steepest slope is precisely the greatest velocity so steepest slope all right which is equals greatest velocity greatest velocity is when all of the energy is kinetic energy okay and then we can see if we look at the slope again and remember that get on in position versus time graph the slope always represents velocity right here right we have points in the motion of our oscillating spring where the slope is zero that's zero velocity because those are the moments where all of the energy is elastic potential and none of it is kinetic because the velocity is momentarily zero that's when the mass that comes to rest when it's changing directions and springs back the other way okay so this this motion has um terms that we've seen a bit before when we talked about orbits because orbits repeat and they have a period of repetition so does the cyclic process of a bouncing spring okay the frequency is just the reciprocal of the period it's just one over t right and it's just how many times the process repeats per second if you have something that takes more than a second to repeat then it actually has a frequency that's less than one so like a frequency of 0.25 right so if i say f equals 0.25 hertz those are the units of frequency which is just one over time well then the period is just one over that so that would just be one over 0.25 and then i'm going to rewrite the units as inverse seconds or one over seconds so you can clearly see that when we do all this seconds come back up to the numerator and our final value will be four seconds so a process that takes four seconds to repeat would would have a frequency of 0.25 hertz okay and the amplitude is just how far from equilibrium the in this case the spring gets and if if we're going to be using the same sort of comparison to um a pendulum then it would just be how you know how far um how far it swings okay usually then we would express it as an angular quantity rather than a displacement right here it's going to be a displacement though because your spring is back and forth very one-dimensional no angles okay all right so that's the amplitude that's just how far from equilibrium the bounces right so the amplitude and the previous figure would have been exactly this value here right because amplitude is measured in meters so the amplitude would be this distance here that would be a all right hopefully that looks good okay so when you have uh when you have this whole process it's because the spring experiences that force that same force we saw before okay and it follows hooke's law that force is known as a restoring force and i said it's a linear relationship here that here it is described in a sentence a restoring force that increases in direct proportion that means linear to the distance from equilibrium equilibrium results in simple harmonic motion okay that's the term given to this type of sinusoidal motion if it looks like a sine curve or a cosine curve right well then what you get is you get simpler harmonic motion pendulums and springs are both simple harmonic motions okay they are systems that undergo simpler harmonic motion all right so the acceleration is not constant it can't be because think about the velocity is constantly changing the rate at which which the velocity is constantly changing is itself not constant that's the whole idea of acceleration not being constant and you you can think about that because of i mean just think about the the curve right because remember the velocity is the slope right does the slope change at a gradual rate here no right the only way the slope would change at a gradual rate is if the position versus time graph was a parabola okay but it's not this is not a parabola therefore the acceleration is not constant okay mathematically it is as simple as that okay and back to bring this back to the potential energy we saw elastic potential energy is just one half kx squared okay that's the energy that's stored in the spring okay so the spring constant k is a measure of how stiff it is higher k as i said before is a stiffer spring that's going to take more force to displace okay and x is just the distance from equilibrium okay all right so that wraps it up