# Definition:Simple Harmonic Motion/Frequency

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## Definition

Consider a physical system $S$ in a state of simple harmonic motion:

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

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 denoted as

Some sources use $f$ to denote a **frequency**, but as $f$ is also often used to denote a general function, this could cause confusion and is not recommended.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.20$: Vibrations in Mechanical Systems