Assume a particle is moving with simple harmonic motion with its position governed by the equation

The velocity of the particle is defined to be the derivative . We define the frequency of the motion to be the reciprocal of the period.

Find the equation of motion of the particle if and when and if the period is .

We have that the period is this implies . So, the equation of motion is

Then using the given conditions,

and

These two equations give us

Therefore,