Definition:Natural Frequency

Definition

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

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

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

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

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

$\nu = \dfrac 1 T$

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

Also see

• Natural Frequency of Underdamped System

Sources

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