Question

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 maximum for $\omega = \omega_2$, then

• A. $\omega_1 \ne \omega_0$ and $\omega_2 = \omega_0$
• B. $\omega_1 = \omega_0$ and $\omega_2 = \omega_0$
• C. $\omega_1 = \omega_0$ and $\omega_2 \ne \omega_ 0$
• D. $\omega_1 \ne \omega_0$ and $\omega_1 \ne \omega_0$

Answer 1

Answer: (B)

$\omega_1 = \omega_0$ and $\omega_2 = \omega_0$

Answer 2

The amplitude and velocity resonance occurs at the same frequency.
At resonance, i.e $\omega_1 = \omega_0$ and $\omega_2 = \omega_0$ the amplitude and energy of the particle would be maximum.