A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force $F\sin \omega t$. If the amplitude of the particle is maximum for $\omega = {\omega _1}$ and the energy of the particle is maximum for $\omega = {\omega _2}$, then (where ${\omega _0}$ natural frequency of oscillation of particle)
AIPMT 1998, Medium
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(c) Energy of particle is maximum at resonant frequency i.e., ${\omega _2} = {\omega _o}$. For amplitude resonance (amplitude maximum) frequency of driver force $\omega = \sqrt {\omega _o^2 - \left(\frac{b}{2m} \right) ^2} $
The amplitude and velocity resonance occurs at the same frequency.
At resonance,i.e. ${\omega _1} = {\omega _o}$ and ${\omega _2} = {\omega _o}$ the amplitude and energy of the particle would be maximum.
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