(a) A mass of 20 g stretches a spring 5 cm. Suppose that

(a) A mass of 20 g stretches a spring 5 cm. Suppose that the mass is also attached to a viscous damper with a damping constant of 400 dyne?s/cm. If the mass is pulled down an additional 2 cm and then released, find its position y at any time t. Plot y versus t. Determine the quasi-frequency and the quasi-period. Determine the ratio of the quasi-period to the period of the corresponding undamped motion. Also find the time ? such that ?y(t)? < 0.05 cm for all t > ?. (b) Draw a phase portrait of the equivalent dynamical system that includes the trajectory corresponding to the initial value problem in part (a).