Definition:Simple Harmonic Motion

Definition
Consider a physical system $S$ whose motion can be expressed in the form of the following equation:
 * $x = A \sin \left({\omega t + \phi}\right)$

where $A$ and $\phi$ are constants.

Then $S$ is in a state of simple harmonic motion.

Also defined as
Simple harmonic motion can also be characterised in the form:
 * $x = A \cos \left({\omega t + \phi}\right)$

From Sine of Angle plus Right Angle:
 * $\sin \left({\omega t + \phi + \dfrac \pi 2}\right) = \cos \left({\omega t + \phi}\right)$

the two forms can be seen to be equivalent.

Also known as
Simple harmonic motion can also be referred to as simple harmonic oscillation or simple harmonic vibration.

Some sources abbreviate it to SHM.