An oscillator of mass m executes x = x0 sin(omega t) under a driving force F = F0 cos(omega t). The damping (resistive) force depends on velocity as F_res = -gamma m v. Determine the damping coefficient gamma.

F0/(x0 omega)
F0/(2 x0 omega)
F0/(m x0 omega)
F0/(2 m x0 omega)

Correct answer: F0/(m x0 omega)

Solution

Average input power = <F0 cos(omega t) * x0 omega cos(omega t)> = F0 x0 omega/2. Average dissipated power = <gamma m v²> = gamma m x0² omega²/2. Equating gives gamma = F0/(m x0 omega).

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