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). 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 (a) 3b1, and (b) b1/2.

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). 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 (a) 3b1, and (b)  b1/2.