A sinusoidally varying driving force is applied to a damped harmonic oscillator

Question

A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b1, the amplitude is A1 when the driving angular frequency equals k/m . (a) In terms of A1, what is the amplitude for the same driving frequency and the same driving force amplitude Fmax, if the damping constant is 6b1? (b) In terms of A1, what is the amplitude for the same driving frequency and the same driving force amplitude Fmax, if the damping constant is b1/8?

Explanation / Answer

F = Fo * sinwt

w = sqrt(k/m)

=> A = Fo/[b *sqrt(k/m)]              ----------------> amplitude

a)    if the damping constant is 6b1

=>    amplitude = A1/6

b)    if the damping constant is b1/8

=>    amplitude = 8A1

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