A ball falls from a height 'h' above the ground, collides and rebounds. The collision is perfectly elastic. At every moment the ball was moving under gravity and so has mg force downward i.e., towards the point of contact. Is mg "restoring force” in this motion. If yes, then is this motion SHM?
False
The motion repeats itself after equal intervals of time. Hence, no doubt it is periodic. But can mg be called a restoring force? Let's analyze this.
I consider the contact point to be the position of equilibrium (Normal reaction balancing mg), restoring force is usually dependent on displacement from mean position. If the displacement is zero, restoring force must be zero. However, the force of gravity on the body never goes to zero during its motion.
So mg cannot be the restoring force.