Definition:Resonance Frequency

Definition

Consider a second order ODE in the form:

$\dfrac {\d^2 x} {\d t^2} + 2 b \dfrac {\d x} {\d t} + a^2 x = K \cos \omega x$

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

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.20$: Problem $1$