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  • Hi. It's Mr. Andersen and this AP Physics essentials video 44. It is on simple harmonic

  • motion. Imagine we take an object that is in equilibrium and we push on it. But it does

  • not just move away. There is a restoring force that returns it towards equilibrium and another

  • returning force that returns it towards equilibrium. And so what we get is this simple harmonic

  • motion. What would be an example of this? Pushing a child on a swing. And so there are

  • really two examples we will do in AP Physics. One is the mass spring oscillator. And so

  • it is going to bounce up and down like this. Or a pendulum that is going to swing back

  • and forth like this. So equilibrium is going to be right in the middle. But these restoring

  • forces continue to bring it back towards equilibrium. And so if you have an object moving towards

  • equilibrium based on restoring forces we call that simple harmonic motion. And so here are

  • the two types we will talk about in AP Physics. Now an important characteristic with each

  • of these is the period of that harmonic motion. Period is always going to be measured in seconds

  • and it its time. So it is the time it takes on this oscillating spring to move from here

  • to bounce up and then to bounce back again. Or for a pendulum to swing from here over

  • to here and then back again. And so in a mass spring oscillator how do we increase the period?

  • Well the easiest way to do that is simply increase the mass. As we increase the mass

  • hanging from the spring the period is going to get longer. How do we decrease it? Well

  • we can change the stiffness of the spring. As we make it stiffer then we are going to

  • make that period go down. What about a pendulum? How do we increase the period of a pendulum?

  • Well we do that by just simply changing the length of the pendulum. Now what is interesting

  • about pendulums is the mass does not have anything to do with it. And so how do we then

  • decrease the period of the pendulum? Well we have to change the gravitational field

  • strength. As we increase that field strength then we are going to decrease the period.

  • And so with both of these forms of simple harmonic motion you should be able to identify

  • the position of the object at any time, its relative velocity and acceleration. And figure

  • out when these are at a maximum and when they are at a minimum. And so let's look at some

  • simple harmonic motion. This one we have it horizontal with two springs. And so we can

  • see it is its motion. Equilibrium is going to be right in the middle. And so as I pull

  • it towards this side there is going to be tension in this spring right here. And it

  • is going to pull it towards the right. And so that restoring force is going to move it

  • towards equilibrium. Now it is going to move in that direction. Now this other spring is

  • going to move it back towards equilibrium like that. And so what we are going to get

  • is this simple harmonic motion. What is cool about this one is there is an accelerometer

  • with little LEDs so you can see the acceleration of the object. You can see right in the middle

  • there is no acceleration, right in the middle. And so what do you have to do in videos like

  • this, or in problems like this? You have to be able to identify the position of the object

  • and the velocity and the acceleration. When are they at a maximum? When are they going

  • to be at a minimum. So let's use this scenario. And so I am going to pull that object towards

  • the left. And so now I have let it go. And so at this point, right here, as it is starting

  • to move, where is our position going to be be? It is going to be maximum towards the

  • left. What about our velocity at this point? It is going to be minimum. It is going to

  • be zero. And what is going to be our acceleration? Our acceleration is going to be maximum towards

  • the right. We are going to have great acceleration at this point. Let's let it go for a second.

  • And I have paused it again here, right in the middle. What is our position? Again it

  • is minimum. It is at zero. What is our velocity? Well it is accelerated. And now our velocity

  • is at a maximum at this point. What is our acceleration? There is no acceleration right

  • when it is in the middle. Let's let it go again. It is going to move over to this side.

  • Now our position if maximum to the right. What about velocity? It is back to zero again.

  • Where is our acceleration? It is going to be maximum now towards the left. And so let's

  • do some little experimentation with a mass spring oscillator. We are using a PHET simulation.

  • And let's look at how the mass and that stiffness of the spring affect the period. And so I

  • am going to take a weight and put it on here. Then we will measure the period. Just qualitatively.

  • So that is going to be the period. So it is a 50 gram mass. Now let's put a 100 gram mass

  • on there. And let's listen to the period again. Okay. So you can see we are slowing down the

  • period as we increase mass. Let's put 250 grams on there. So you can see that as we

  • increase the mass on that spring then we are increasing the period. But now let's play

  • around with the stiffness of the spring. We call that the spring constant. So now I have

  • made it a stiffer spring. I put that 250 gram mass on it. And you can see the period is

  • now decreasing. And so by increasing the stiffness of the spring we are decreasing the period

  • of the spring. Now let's really make it a soft spring. What happens? You can see the

  • period get really really really large. And so in summary what have we learned just from

  • this experimentation? That if you increase mass you are going to make a longer period

  • for that harmonic motion. And if we increase the stiffness then we are going to make it

  • a shorter period. If we look at that quantitatively, so if we look at the actual period of a spring

  • like this, what is really affecting it are two things, the mass and the spring constant.

  • And so you can imagine just looking at this algebraically, if we increase mass what is

  • going to happen to the period? The period is going to increase because it is in the

  • numerator. What is going to happen if we increase the constant of the spring or the spring constant?

  • We make it stiffer, as this number gets larger in the denominator, then we see that the period

  • is going to become less. Now let's look at a pendulum. Again another PHET simulation.

  • So I am going to move this to the side. I am going to try to drop it at about a 30 degree

  • angle. And this one has a little photo gate timer so I can time how long it takes to get

  • back to that original position. So we can see here that we have a period of 2.862. Now

  • I am going to make the pendulum have a smaller length, dropping it from the same angle. And

  • you can see that the period now is less. It is 2.415. Now let me make it even less. I

  • am going to try to drop that weight again at a 30 degree angle. Set my photo gate timer

  • and you can see that the period is becoming less. So as we decrease the length, what are

  • we doing to it? We are speeding it up. Or the period is decreasing. Now watch what happens

  • as I change the mass now. As I change the mass, drop it from a 30 degree angle, start

  • my photo gate timer you can see that it does not affect it. So mass does not affect the

  • period. But what does remember is going to be the gravitational field strength. So now

  • let me change it to the moon. And you can see that they period is increasing. It is

  • slowing down. Let me change it to earth. Now it is speeding up. What happens if we make

  • it Jupiter? It is really speeding up. Or if we make it nothing, it just continues moving

  • like that. So if we look at that quantitatively as we, or rather qualitatively, as we increase

  • the length we have a longer period. And as we increase the gravitational field strength

  • then we have a shorter period. If we look at that algebraically this is the equation.

  • Length is going to be on the top remember. And so as we increase the length, we are going

  • to increase the period of the pendulum. What happens as we increase gravitational field

  • strength? As we increase that then we are going to decrease the overall period of the

  • pendulum. Okay. Did you learn to predict which properties affect harmonic motion? Again it

  • is a restoring force moving it back towards equilibrium. Could you design and plan and

  • collect data to ascertain what characteristics are affecting the period? Again in a spring

  • it is going to be the mass and the stiffness of the spring. If we are looking at a pendulum

  • it is going to be the length and the gravitational field strength. And finally could you figure

  • that out quantitatively? What happens as we increase length for example to our period,

  • or gravitational field strength? Well I hope so. And I hope that was helpful.

Hi. It's Mr. Andersen and this AP Physics essentials video 44. It is on simple harmonic

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