Page History

Excerpt
The frequency that is characteristic of a given freely oscillating system, with no applied driving force.

If the frequency is is in oscillations per unit time, it is represented by the symbol ν₀. The angular natural frequency is a measure of the angle per unit time, assuming that one full cycle is equal to a full rotation around a circle. This frequency is represented by the symbol ω₀, and is often measured in radians per second. If that is the case, then the relationship between the two forms is

Latex
\begin{large} \[\omega_{0} = 2 \pi \nu_{0} \]\end{large}

For a mass on a spring, the natural frequency is given by

Latex
\begin{large} \[ \omega_{0} = \sqrt{\frac{k}{m}} \]\end{large}

while for a simple pendulum of mass m on an arm of length L the natural frequency is

Latex
\begin{large} \[ \omega_{0} = \sqrt{\frac{g}{L}} \]\end{large}

See Simple Harmonic Motion for fuller details.

The natural frequencies are related to the period T by:

Latex
\begin{large} \[ T = \frac{1}{\nu_{0}} = \frac{2 \pi}{\omega_{0}} \]\end{large}