Q. A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force. $F = F_{0}\sin{\omega t}$ 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
A) $\omega_{1} = \omega_{0}\ and\ \omega_{2} \neq \omega_{0}$
B) $\omega_{1} = \omega_{0}\ and\ \omega_{2} = \omega_{0}$
C) $\omega_{1} \neq \omega_{0}\ and\ \omega_{2} = \omega_{0}$
D) $\omega_{1} \neq \omega_{0}\ and\ \omega_{2} \neq \omega_{0}$
Explanation
(c) Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped maximum vibrations. Velocity resonance takes place ($ie$, maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.