Pendulum Motion and Simple Harmonic Approximation

Technically the movement of a pendulum doesn’t quite match simple harmonic motion.

However, if the angle theta is small enough,  θ~sin(θ)

In fact for angles less than 15 degrees the error will be less than one percent.

Thus a simple pendulum essentially displays SHM (simple harmonic motion).

Such approximations are very useful in certain applications, especially in engineering, where such a small amount of error can be tolerable.