(Solved): 4. An object of mass \( 0.2 \mathrm{~kg} \) is hang from a spring whose spring constant is \( 80 \m ...

4. An object of mass \( 0.2 \mathrm{~kg} \) is hang from a spring whose spring constant is \( 80 \mathrm{~N} / \mathrm{m} \). The body is subject to a resistive force given by \( -b v \), where \( v \) is the velocity in \( \mathrm{m} / \mathrm{s} \) and \( \mathrm{b}=4 \mathrm{~kg} / \mathrm{s} \). a) (12 points) Set up the differential equation of motion for free oscillations of the system, and find the period of such oscillations b) (12 points) The object is subjected to a sinusoidal driving force given by \( F_{0} \) coswt, where \( F_{0}=2 \mathrm{~N} \) and \( \omega=30 \mathrm{~Hz} \). In the steady state, what is the amplitude of the forced oscillation?