# Definition:Natural Frequency

## Definition

Consider a physical system $S$ whose behaviour can be described with the second order ODE in the form:

$(1): \quad \dfrac {\mathrm d^2 x} {\mathrm d t^2} + 2 b \dfrac {\mathrm d x} {\mathrm d t} + a^2 x = 0$

for $a, b \in \R_{>0}$.

Let $b < a$, so as to make $S$ underdamped.

The natural frequency $\nu$ of $S$ is defined as:

$\nu = \dfrac 1 T$

where $T$ is the period of the oscillation of $S$.