# Definition:Simple Harmonic Motion

## Definition

Consider a physical system $S$ whose motion can be expressed in the form of the following equation:

$x = A \map \sin {\omega t + \phi}$

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

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

### Amplitude

The parameter $A$ is known as the amplitude of the motion.

### Period

The period $T$ of the motion of $S$ is the time required for one complete cycle:

$T = \dfrac {2 \pi} \omega$

### Frequency

The frequency $\nu$ of the motion of $S$ is the number of complete cycles per unit time:

$\nu = \dfrac 1 T = \dfrac \omega {2 \pi}$

## Also defined as

Simple harmonic motion can also be characterised in the form:

$x = A \map \cos {\omega t + \phi}$
$\map \sin {\omega t + \phi + \dfrac \pi 2} = \map \cos {\omega t + \phi}$

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.