Characteristic of force for simple harmonic motion:
If the acceleration of an oscillating particle is proportional to distance from its equilibrium position and always towards the equilibrium position, then that motion of the particle is called simple harmonic motion.
(i) It is a special type of force acting on a particle having simple harmonic motion.
(ii) In case of this motion acceleration of the particle and magnitude of the force acting on it is proportional to the displacement.
(iii) Direction of the acceleration and force acting on the particle always remains towards the equilibrium, i.e., in the opposite direction of displacement.
(iv) Direction of force in this type of motion is linear.
A restoring force must act on the body. Body must have acceleration in a direction opposite to the displacement and the acceleration must be directly proportional to displacement.
Obviously, all the periodic motions do not have those characteristics. So, all simple harmonic motions are periodic motions but all periodic motions are not simple harmonic motions.