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(D) For a damped forced oscillator,the amplitude $A$ is given by $A = \frac{F_0}{\sqrt{m^2(\omega_0^2 - \omega^2)^2 + b^2\omega^2}}$.The amplitude is

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$\omega_{1} < \omega_{2}$

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(D) For a damped forced oscillator,the amplitude $A$ is given by $A = \frac{F_0}{\sqrt{m^2(\omega_0^2 - \omega^2)^2 + b^2\omega^2}}$.The amplitude is maximum when the denominator is minimum,which occurs at $\omega_1 = \sqrt{\omega_0^2 - 2\gamma^2}$,where $\gamma = \frac{b}{2m}$.The energy of the oscillator is proportional to the square of the amplitude $(E \propto A^2)$.The energy is maximum when the amplitude is maximum,which occurs at $\omega_2 = \omega_0$ (the natural frequency) in the context of power absorption,or specifically,the resonance frequency for energy is $\omega_2 = \omega_0$.Comparing the two,since $\omega_1 = \sqrt{\omega_0^2 - 2\gamma^2}$,it is clear that $\omega_1 Therefore,$\omega_1 < \omega_2$.

In forced oscillation of a particle,the amplitude is maximum for a frequency $\omega_{1}$ of the driving force,while the energy is maximum for a frequency $\omega_{2}$ of the driving force. Then:

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