 Now we can take a look at pendulum simple harmonic motion. And we're going to take the case of a simple pendulum. Now over here I've got a simple pendulum animation going. And there's a couple of properties that need to be in place for us to be a simple pendulum. One is it must be a thin string, meaning it's not a lot of mass in that string, not a lot of inertia. But the length of the string matters. And I can either use the symbol of little l or big l to represent the length of that string. You'll see both of those in different textbooks. There's got to be a mass out on the end of that string. And I'm going to give it the symbol of m. And the last thing is it has to be a small amplitude. What does that mean? Well imagine I take my pendulum here and I draw an imaginary line straight down. And so I'm watching it oscillate back and forth to one side and then the other. The amplitude is sort of the angular measurement of how far angle wise it goes from one side to the other. And that needs to be a small angle. Now we know to have simple harmonic motion we have to have a restoring force. So if I look at the forces on the pendulum which are tangent to the path and I look at the angular acceleration, I end up finding that the angular acceleration is approximately equal to minus g over l theta. I'm not showing you in this particular video how we came up with that equation. Now this approximation here is a pretty good approximation for small angles. That's why our simple pendulum had to have a small amplitude. And by small angles we really mean something which is less than about 0.2 radians which is about 10 degrees just to give you a feel for that. Now looking at this equation I've got my acceleration and my position. In this case it's angular acceleration and angular position. I've got gravity as my g, my length which is my l and those things are constants for a particular problem. And I've got a negative sign in there and we have to have that negative sign for it to be a restoring force. So this is of the form of the restoring force we need for simple harmonic motion. Now since we know it's simple harmonic motion it's going to oscillate with an equation similar to our general one. Although we have a few differences in here. My position is not x anymore it's the angular position theta. I've still got it being a function of the variable time. Now instead of having a capital A I'm using my theta max to represent my angular amplitude. But I still have an angular frequency and a phase just like my general equation. Now in terms of my pendulum's omega value or its angular frequency because this was my equation for the acceleration remember that the negative sign out front tells me it's a restoring one. I needed to have some problem specific constants and in this case it's g over l. So my omega squared for this particular problem is g over l. Or I could write that as omega is the square root of g over l. Now remember that omega is the angular frequency. My g is gravity and l is the length. So for any particular pendulum once you decide whether it's on earth or the moon or wherever it is you know your gravity value. Once you set the length of that pendulum that means the angular frequency is set by those objects. So now we can talk about the pendulum period. Remember that the period is related to the angular frequency by 2 pi over omega. And since my omega was the square root of g over l that means I could represent my period as 2 pi the square root of l over g. Because my omega was on the bottom it flips my fraction. That means a longer length is going to result in a longer period. And if I could somehow alter the gravity that would also alter the period of the pendulum. So that's a pendulum operating in simple harmonic motion. Just a brief introduction to the simple one.