What conditions must be met to produce simple harmonic motion?

Hooke’s Law states that the force required to stretch or compress an elastic object is directly proportional to the change in length or displacement of the object.

A body executes simple harmonic motion when it oscillates back and forth about it is in equilibrium. If the net force is described by Hooke’s law, then the body will oscillate with equal displacement on either side of the equilibrium position because the force always gets directed towards the center.

Thus, the net force must obey Hooke’s law

If there is damping (by friction or any other external phenomenon), the oscillation on either side will keep on reducing and a time will come when the oscillation will stop. Hence, there should be no damping to produce simple harmonic motion.

Thus,there must not be any Damping force acting on the system.