# Module 4.3: Simple Pendulum

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This model demonstrates the motion of a simple pendulum. A simple pendulum is a model that assumes that friction does not exist, the string of the pendulum has no mass and all of the mass of the bob at the end of the pendulum is concentrated at the point. Once we get those limitations out of the way, we're free to focus on the angles formed by the pendulum.

This model measures the angle, angular velocity and angular acceleration. The initial angle from which the pendulum is dropped and pendulum length are controlled by sliders. The acceleration of the angle is a function of the gravity constant times the sine of the angle, divided by the length of the string that the pendulum is on. While the initial angular velocity is 0, angular acceleration feeds that stock. When the model is running, you can see very clearly on the graph that the velocity is derived from the angular acceleration and the angle itself is the derivative of the angular velocity.

This graph provides a beautiful example of simple harmonic motion (as well as a great refresher on calculus!).