What is the formula of the Amplitude in forced oscillation ??

Let  $f_t=f_{0}\sin \omega_d t$ be an additional periodic force apart from the restoring force and the damping force,

then Amplitude in forced oscillation given by

$A= \frac{f_{0}/m}{\sqrt{\left ( \omega_d ^{2}-\omega {_{0}}^{2} \right )^{2}+\left ( \frac{b\omega_d }{m} \right )^{2}}}$

Where   $\omega _{0}= \sqrt{K/m}$  is called a natural angular frequency.

and  $\omega_d$ is the angular frequency of the driving force.

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