When will the motion of a simple pendulum be simple harmonic?

When will the motino of a simple pendulum be simple harmonic?

When the motion of a simple pendulum will be simple harmonic?

The motion of a simple pendulum is

Show that motion of a simple pendulum is simple harmonic.

Show that for a small oscillations the motion of a simple pendulum is simple harmonic. Derive an expression of its time period.

Show that the motion of a simple pendulum is simple harmonic for small amplitudes of oscillation.