Definition:Simple Harmonic Motion

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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.


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:

$x = A \cos \left({\omega t + \phi}\right)$

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.


Sources