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hi it's mr. Andersen and this is ap

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

physics essentials video 44 it's on

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

simple harmonic motion imagine we take an object that's in equilibrium and we push on it but it doesn't just move away

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

there's 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

returning force that returns it towards equilibrium and so what we get is this

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

simple harmonic motion what would be an example of this pushing a child on a swing and so there are really two

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

examples will do in AP Physics one is a mass spring oscillator and so it's going

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

to bounce up and down like this or a

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

pendulum that's going to swing back and forth like this so equilibrium is going to be right in the middle

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

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

equilibrium based on restoring forces we call that simple harmonic motion and so

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

here are the two types we'll talk about in AP physics now an important

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

characteristic with each of these is the period of that harmonic motion period is

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

always going to be measured in seconds and it's time so it's the time it takes on this oscillating spring to move from

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

here to bounce up and then to bounce back again or for a pendulum to swing

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

from here over to here and then back again and so in a mass spring oscillator how do we increase the period well the

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

easiest way to do that is simply increase the mass as we increase the

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

mass hanging from the spring the period is going to get longer how do we

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

decrease it well we can change the stiffness of the spring as we make it

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

stiffer then we're going to make that period go down what about a pendulum how do we increase the period of the

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

pendulum well we do that by just simply changing the length of the pendulum now

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

what's interesting about pendulums is the mass doesn't have anything to do with it and so how do we then decrease

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

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.

strength as we increase that field strength and we're going to decrease the

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

period and so with both of these forms of simple harmonic motion you should be

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

able to identify the position of the object at any time its relative velocity and acceleration and figure out when

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

these are at a maximum and when they're 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

simple harmonic motion this one we've got it horizontal with two Springs and

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

so we see 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

it towards this side there's going to be tension in this spring right here and

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

it's going to pull it towards the right and so that restoring force is going to

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

move it towards equilibrium now it's going to move in that direction now this

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

other spring is going to move it back towards equilibrium like that and so

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

what we're going to get is this simple harmonic motion what's cool about this one is there's an accelerometer with

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

little LEDs so you can see the acceleration of the object you can see

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

right in the middle there's 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

this or in problems like this you have to be able to identify the position of

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

the object and the velocity and acceleration when are they at a maximum

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

when are they going to be at a minimum so let's use this scenario and so I'm

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

going to pull the object towards the left and so now I've let it go and so at this point right here as it's starting

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

to move where's our position going to be it's going to be maximum towards the

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

left what about our velocity at this point it's going to be minimum it's

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

going to be zero and what's going to be our acceleration our acceleration is going to be maximum towards the right

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

we're going to have great acceleration at this point let's let it go for a

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

second and I've paused it again here right in the middle what's our position

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

again it's minimum it's at zero what's our velocity well its accelerated

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

and now our velocity is at a maximum at this point what's our acceleration there's no acceleration right when it's

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

in the middle let's let it go again it's

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

going to move over to this side now our position is maximum to the right what about velocity it's back to zero again

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

where's our acceleration it's going to be maximum now towards the left and so

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

let's do some little experimentation with the mass spring oscillator we're

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

using a Phe T simulation and let's look at how the mass and that stiffness of the spring affect the period and so I'm

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

going to take weight put it on here and then we'll measure the period just qualitatively so that's going to be the

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

period so that's a 50 gram mass now

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

let's put a hundred gram mass on there and let's listen to the period again okay so you can see that it's we're

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

slowing down the period as we increase mass let's put 250 grams on there so you can see that as we increase the

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

mass on that spring then we're 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

around with the stiffness of the spring we call that the spring constant so now

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

I've made it a stiffer spring I put that 250 gram mass on it and you can see the

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

period is now decreasing and so by increasing the stiffness of the spring we are increasing the or decreasing the

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

period rather of the spring now let's really make it a soft spring what

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

happens you can see the period gets really really large and so in summary

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

what have we learned just from this experimentation that if you increase mass you're going to make a longer

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

period for that harmonic motion and if we increase the stiffness then we're

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

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.

like this what's really affecting it are two things the mass and the spring

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

constant and so you can imagine just looking at this algebraically if we

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

increase mass what's going to happen to the period the period is going to

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

increase because it's in the numerator what's going to happen if we increase the constant of the spring or the spring

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

constant as we make it stiffer as this number gets larger in the denominator

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

then we see that the period is going to become less now let's look at a pendulum again another Paet simulation so i'm

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

going to move this to the side i'm 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

angle and this one has a little photo gate timer so i can time how long it takes back or 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

back to that original position so we can see here that we've got a period of 2.86

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

- now i'm going to make the pendulum have a smaller length dropping it from

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

the same angle and you can see that the period now is less it's two point four one five now let me make it even less

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

I'm going to try to drop that weight again at a 30-degree angle set my photo

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

gate timer and you can see that the period is becoming less so as we

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

decrease the length what are we doing to it we're speeding it up or the period is decreasing now watch what happens as I

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

change the maths now as I change the mass drop it from a 30-degree angle

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

start my photo gate timer you can see that it doesn't affect it so mass

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

doesn't affect the period but what does remember is going to be the gravitational field strength so now let

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

me change it to the moon and you can see that the period is inked

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

it's slowing down let me change it to earth now it's speeding up what happens

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

if we make it Jupiter it's really speeding up or if we make it nothing it

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

just continues moving like that so if we look at that quantitatively as we were rather qualitatively as we increase the

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

length we got a longer period and a zinc as we increase the gravitational field

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

strength then we got a shorter period if we look at that algebraically this is

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

the equation length is going to be on the top you remember and so as we increase the length we're going to

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

increase the period of the pendulum what happens as we increase gravitational

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

field strength as we increase that then we're going to decrease the an overall

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

period of the pendulum okay did you learn to predict which properties effect harmonic motion again

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

it's a restoring force moving it back towards equilibrium could you design and

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

plan and collect data to ascertain what characteristics are affecting the period again in a spring it's going to be the

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

mass and the stiffness of the spring if

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

we're looking at a pendulum it's going to be the length and the gravitational field strength and finally could you

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

figure that out quantitatively what happens as we increase length for example to our period or gravitational

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

field strength well I hope so and I hope that was helpful

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