\begin{definition}[Definition:Natural Frequency]
Consider a physical system $S$ whose behaviour can be described with the second order ODE in the form:
:$(1): \quad \dfrac {\d^2 x} {\d t^2} + 2 b \dfrac {\d x} {\d t} + a^2 x = 0$
for $a, b \in \R_{>0}$.
Let $b < a$, so as to make $S$ underdamped.
:600px
The '''natural frequency''' $\nu$ of $S$ is defined as:
:$\nu = \dfrac 1 T$
where $T$ is the period of the oscillation of $S$.
\end{definition}