\begin{definition}[Definition:Forced Vibration]
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 $S$.
\end{definition}