Definition:Simple Harmonic Motion/Period

Definition
Consider a physical system $S$ in a state of simple harmonic motion:
 * $x = A \sin \left({\omega t + \phi}\right)$

The period $T$ of the motion of $S$ is the time required for one complete cycle:
 * $T = \dfrac {2 \pi} \omega$

Also see

 * Sine and Cosine are Periodic on Reals