Question

Which is a necessary and sufficient condition for simple harmonic motion?

Answer 1

Simple harmonic motion:

1. Frictional forces are absent in harmonic oscillations. These oscillations possess constant amplitude.
2. Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position.
3. The back and forth, repetitive movements of the swing against the restoring force is the simple harmonic motion.

An illustrative diagram of the simple harmonic motion is shown below.

1. The necessary condition for simple harmonic motion is the restoring force must be proportional to the displacement and act opposite to the direction of motion with no drag forces or friction.
2. If $F$ is the restoring force and $x$ is the displacement from the mean position then

$F\propto \left(-\mathrm{x}\right)$

The negative sign represents that action is in opposite direction.