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.