Definition:Resonance Frequency

Definition
Consider a second order ODE in the form:
 * $\dfrac {\mathrm d^2 x} {\mathrm d t^2} + 2 b \dfrac {\mathrm d x} {\mathrm d t} + a^2 x = K \cos \omega x$

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

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

Let the forcing frequency $\omega$ be such that $S$ is in resonance.

Then $\omega$ is known as the resonance frequency.

Also known as
Some sources refer to this as the resonant frequency

Also see

 * Condition for Resonance in Forced Vibration of Underdamped System‎