 pendulum here so I thought it would be a good time to talk about how to find the period and restoring force of an object moving in simple harmonic motion like this one. Hey are you gonna do any kinds of calculations that thing? Oh hi everyone this is my graph and calculator graphy. Well sure yeah we're gonna take a look at two different calculations here today to explain the pendulum. Okay well I'll stay here and help. Sure why not. Recall that simple harmonic motion is any type of repetitive motion driven by a force. That force is called the restoring force. In a mass spring system the restoring force was the force in the spring. But when we're talking about a pendulum there's no spring to provide the restoring force so what force makes the pendulum move? I have no idea. All right well let's make a free body diagram. Let's take a look at this diagram of a pendulum pulled back to its maximum displacement from equilibrium this is called the amplitude of the pendulum. At this point in time the forces acting in the pendulum are the force of gravity and the force of tension. If we move these forces around a little put them tip to tail so they're added together we see that the total of these two forces make up a force that points down and to the left. This is the force makes the pendulum start moving left. This is the restoring force. Do you think we should calculate the restoring force? Oh yeah. In our diagram the angle between the string and the starting point of the pendulum is the same as the angle at the top of the free body diagram. So the restoring force which is the opposite side of that triangle can be calculated by multiplying the hypotenuse force of gravity by the sign of the angle. This gives us our formula for restoring force in a pendulum. Restoring force is equal to the force of gravity times sign of the angle theta. Hey that formula isn't on my formula sheet. That's right that formula isn't on your data sheet. So you'll have to either remember it or work it out from the free body diagram for a test. Can I put any angle into this formula? Actually it's interesting you can't put any angle into that formula. The maximum angle that works in the formula is 15 degrees and that's because when the pendulum is pulled back any further than 15 degrees it actually does a little bit of a free fall drop downwards before it starts this pendulum motion. So anything over than 15 degrees in the pendulum doesn't make an ideal pendulum motion. So the formula doesn't work anymore. Wait I was promised a second formula. Right let's get to that second formula. The period of a pendulum can be calculated using the formula period equals 2 pi times the square root of L over g where L is the length of the pendulum's string in meters and g is the acceleration due to gravity. The really cool thing about this formula is it doesn't have mass or amplitude the amount I pull it back by in it anywhere. So that means those two things don't have any impact on the period. So that means you can have a light mass, a heavy mass, a large displacement, or a small displacement. If the length of the pendulum is the same they all have the same period. So now you know a little bit more about pendulums. Check out our website for more info. Well it's not really our website. Check out our website.