A mass of 25 kg is attached to the end of a spring; at equilibrium, the spring is 0.5 meters long. The force needed to stretch the spring to a total length of 1 meter is 50 Newtons. If the system is released from this stretched position at time t=0, determine the following: a. Find a differential equation that models the position of the mass on the end of the spring at time t (assume no damping) and solve it. b. If a dashpot is introduced into this system with damping coefficient c= 60 but everything else remains the same, find a differential equation that models the position of the mass on the end of the spring at time t and solve it. Graph the damped and undamped solutions together on the same axes. Determine the amplitude (the amplitude function), "pseudo-frequency", and "pseudo-period" of the damped system. c. Compare these with the "natural" amplitude, frequency, and period of the undamped system. Clearly mark the periods and amplitudes on the graph. Compare the long-term behavior of the systems and explain the difference in periods. In general, do you expect the pseudo-period of a damped system to be larger or smaller than