Wave Mechanics Question 602
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 is maximum for $ \omega ={\omega _{2}} $ , then
Options:
A) $ {\omega _{1}}={\omega _{2}},and,{\omega _{2}}\ne {\omega _{0}} $
B) $ {\omega _{1}}={\omega _{0}},and,{\omega _{2}}={\omega _{0}} $
C) $ {\omega _{1}}\ne {\omega _{0}},and,{\omega _{2}}={\omega _{0}} $
D) $ {\omega _{1}}\ne {\omega _{0}},and,{\omega _{2}}\ne {\omega _{0}} $
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Answer:
Correct Answer: C
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 natural vibrations, i.e. $ {\omega _{2}}\ne {\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}}\ne {\omega _{0}} $ .
BETA
