Definition:Forced Vibration

Definition

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

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

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

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

Then the steady-state motion of $S$ is referred to as forced vibration of $S$.

Forcing Frequency

The frequency:

$\dfrac \omega {2 \pi}$

is known as the forcing frequency of $S$.

Sources

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