Simple harmonic motion is sinusoidal – it can be expressed in terms of
or
functions or a sum ofandfunctions.
or
all imply simple harmonic motion.
If
then we can find the velocity
and the acceleration
by differentiation:
This is illustrated in the diagram below.
Notice that
andhave opposite signs, andis
larger in magnitude.
The displacement leads the velocity by
of a cycle and the velocity leads the acceleration byof a cycle.