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,