Consider the diagram of a simple pendulum.
The bob is displaced through an angle 0 shown.
The restroing torque about the fixed point O is
`tau=-mgsin0`
If 0 is small angle in radians, then `sin0~~0`
`rArrtau~~-mg0rArrtauprop(-0)`
Hence, motion of a simple pendulum is SHM for small angle of oscillations.
