7.5 Simple and Physical Pendulums

Simple

A simple pendulum consists of a point mass attached to a light, inextensible string of length l, swinging under the influence of gravity. When displaced slightly from equilibrium, the pendulum experiences a restoring force due to gravity that pulls it back toward its equilibrium position.

Using the small-angle approximation, ${\sin\theta \approx \theta}$, the restoring force becomes directly proportional to the angular displacement, allowing the motion to be modeled as simple harmonic motion.

Important Equation: ${T_{simple} = 2\pi \sqrt{\frac{l}{g}}}$

${T_{simple}}$ = period of the simple pendulum

${l}$ = length of the pendulum

${g}$ = acceleration due to gravity