Oscillations - Result Question 63
69. A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force $F \sin \omega_0$. 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
(a) $\omega_1=\omega_0$ and $\omega_2 \neq \omega_0$
(b) $\omega_1=\omega_0$ and $\omega_2=\omega_0$
[1989]
(c) $\omega_1 \neq \omega_0$ and $\omega_2=\omega_0$
(d) $\omega_1 \neq \omega_0$ and $\omega_2 \neq \omega_0$
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Solution:
- (c) At maximum energy of the particle, velocity resonance takes place, which occurs when frequency of external periodic force is equal to natural frequency of undamped vibrations, i.e. $\omega_2=\omega_0$.
Further, amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped natural vibrations, i.e., $\omega_1 \neq \omega_0$.
