A body undergoing simple harmonic motion is freely oscillating about a point of

equilibrium, with a restoring

force proportional to its

displacement.

The displacement of the body at a time **t** is its distance from the point of equilibrium. Since it is continually moving, its displacement is always changing and so the magnitude of the restoring force is changing too. It is "restoring" in the sense that it is acting to move the body back toward equilibrium, so while moving away from equilibrium, the body at first decelerates, briefly stops at its maximum displacement, and then heads back the other way, and starts the process in the opposite direction. It is going fastest as it passes through equilibrium and slowest when it briefly stops while at maximum displacement.

At a time **t**, the acceleration, **a**, of a body undergoing SHM can be calculated by **a = - (2π f)**^{2} x, where **f** = frequency (oscillations per second) and **x** = displacement. Note the minus sign in the equation.

This displacement **x** is calculated by either

**x = A sin (2π f t)** if the oscillation started at equilibrium (i.e. it can be represented on a sine curve),

or **x = A cos (2π f t)** if the oscillation started at maximum displacement (it can be represented on a cosine curve).

In both cases, **A** is the amplitude of the oscillation - its maximum displacement. Do not confuse **A**, amplitude, with **a**, acceleration.