The 500 lbf motor is supported on springs with a total stiffness of 5,000 lbf/in. The springs have a damping ratio of 0.07. What is the time expression for the motor response if the excitation/imbalance is given by f(t) = 1 sin(75t)? What is the amplitude of the response and the magnitude of the transmitted force? How does the response and transmitted force change if f(t) = 1 sin(150t)? Plot the magnitude of the transmitted force as a function of operating speed in rpm, assuming a unit force amplitude. On the same plot, re-plot the transmitted force if instead the damping ratio changes to half its original value.