All simple harmonic motinos are periodic motions but all periodice motions are not simple harmonic motions. Explain.

Explanation

Periodic motino is that motion which is repeated identically after a fices interval of time e.g. (i) the revolution of earth around the sun, (ii) the rotation of earth about its own axis etc.
Simple harmonic motion is a special case of periodic motion in which the body moves to and from about its equilibrium position. The force acting on the body at and instant is directed towards equilibrium position and is proportional ot the displacement of th ebody from equilibium position, i.e., `F=-ky`
A simple harmonic motino is represented by a single harmonic function (i.e., sine or cosine function) and of constant amplitude. For example, the oscillations of the bob of simple pendulum is simple harmonic motion which is periodic also. But the revolution of earth around the sun is only periodice and not simple harmonic one, as it is not to and fro motion about a fixed point.