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

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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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