The definition of simple harmonic motion is simply that the acceleration causing the motion *a* of the particle or object is proportional and in opposition to its displacement *x *from its equilibrium position.

Simple Harmonic Motion is closely related to circular motion as can be seen if we take an object that moves in a circular path, like a ball stuck on a turntable. If we consider just the y-component of the motion the path with time we can see that it traces out a wave.

y(t) = A sin(ωt)

This means the the Acceleration of an object that is undergoing simple harmonic motion in has magnitude that is proportional to the object position from the "equilibrium point", but is in the opposite direction.

Simplified; the size of the acceleration depends on the position of the object. The direction of the acceleration is in the opposite direction of the position.

The center line is the equilibrium line