Definition:Simple Harmonic Motion/Frequency

This page is about frequency in the context of simple harmonic motion. For other uses, see frequency.

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
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): angular frequency
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): angular frequency