# 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!).