## Question

A particle, with restoring force proportional to displacement and damping force proportional to velocity is subjected to a force *F* sin ωt. If the amplitude of the particle is maximum at ω = ω_{1} and its energy is maximum at ω = ω_{2}, then (ω_{0} is the angular frequency of natural oscillations of the particle)

### Solution

ω_{1} = ω_{0}, ω_{2 }= ω_{0 }

In resonant oscillations, the amplitude and velocity (and hence energy) maxima occur when the angular frequency ω of the externally applied force equals the angular frequency ω_{0} of the natural oscillations.

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