Question

What conditions must be met to produce simple harmonic motion?

Short answer

(a) The net force must obey Hooke’s law.

(b) There must not be any Damping force acting on the system.

Step-by-step solution

Definition of Hooke’s Law

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.

Relation of Hooke’s law with simple harmonic motion 

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

Relation of Damping with simple harmonic motion

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.