Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

The video tutorial covers the derivation of simple harmonic motion equations for a simple pendulum using calculus. It begins with a review of the pendulum period equation and the definition of a simple pendulum, highlighting assumptions like negligible string mass and point mass bob. The tutorial then derives the restoring force and applies the small angle approximation to simplify equations. It concludes with the derivation of angular frequency and period, and a clarification on the dual meaning of omega in pendulum equations.

What is the general equation that defines simple harmonic motion?

What is the significance of the angle being less than 15 degrees for a simple pendulum?

Describe how the equations for position, velocity, and acceleration for a simple pendulum are derived.

Explain the difference between angular velocity and angular frequency in the context of a simple pendulum.