Definition:Simple Harmonic Motion

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This page is about Simple Harmonic Motion. For other uses, see Harmonic.


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.


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


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

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


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:

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

From Sine of Angle plus Right Angle:

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

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.