Simple harmonic motion is sinusoidal – it can be expressed in terms oforfunctions or a sum ofandfunctions.

orall imply simple harmonic motion.

Ifthen we can find the velocityand the accelerationby differentiation:

This is illustrated in the diagram below.

Notice thatandhave opposite signs, andislarger in magnitude.

The displacement leads the velocity byof a cycle and the velocity leads the acceleration byof a cycle.