A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinωt. If the amplitude of the particle is maximum for ω$$=$$ω$$1$$ and the energy of the particle is maximum for ω$$=$$ω$$2$$, then (where$$ ω$$0$$ natural frequency of oscillation of $$particle)

Question

A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinωt. If the amplitude of the particle is maximum for ω$$=$$ω$$1$$ and the energy of the particle is maximum for ω$$=$$ω$$2$$, then (where$$ ω$$0$$ natural frequency of oscillation of $$particle)

Infinity Learn · Accepted Answer

Energy of particle is maximum at resonant frequency i.e., ω$$2=$$ωo. For amplitude resonance (amplitude$$ $$maximum) frequency of driver force ω$$=$$ω$$o2$$−$$b22m2$$   ⇒ω$$1$$≠ωo

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