The three requirements for
simple harmonic motion are:
- a restoring force
- the system has inertia
- and the acceleration of the bob is directly proportional to its displacement and is always directed to an equilibrium position.
The pendulum has inertial mass
m, the restoring force is the component of the weight along the arc
mg sinθ, and the acceleration is always directed to the lowest position. If the angle is less than 10° then acceleration:
a = -gs/L = -(2πf)2s so
f = (1/2π)√(g/L)