Question

A simple pendulum consists of a particle of mass m suspended by a long, massless wire of length L. Draw a free body diagram for the pendulum bob corresponding to a moment when the bob is located an angular displacement Φ away from (eg. to the right of) equilibrium. Determine an expression in terms of m, g, and Φ for the component of the net force on the bob that points tangent to the path of the bob.

Assume that the pendulum bob undergoes small angular displacements from equilibrium, meaning sinΦ = tanΦ= Φ (radians). Simplify your expression for the tangential component of the net force and use Newton's Second Law to write down the resulting differential equation of motion for the angular position Φ(t) of the pendulum bob as a function of time. Explain how your differential equation of motion implies that the pendulum undergoes simple harmonic motion, and determine the frequency of motion in terms of the given parameters.

Answer 1