An object of mass 0.2 kg is hung from a spring whose spring constant is 80 N/m. The object is subject to a resistive force given by −bv, where v is its velocity in meters per second.
(a) Set up the differential equation of motion for free oscillations of the system.
(b) If the damped frequency is 3/2 of the undamped frequency, what is the value of the constant b?
(c) What is the Q of the system, and by what factor is the amplitude of the oscillation reduced after 10 complete cycles?