Problem #3 A mass M having the velocity Vo = 1 m/sec collides with the bumper as shown in the figure below. The bumper consists of a spring and damper. Use M = 1000 kg and the values of K and B as in Problem 2. In this case, there is no initial compression or extension of the spring, that is, x(0) = 0. We are concerned with the motion of the bumper during the time in which the mass and Vo bumper are in contact. a) For the time during which the mass and bumper are in contact, derive the differential equation describing x(t). b) Solve the equation from part a) to find an analytical expression for the displacement of the mass as a function of time, x(t), for the time during which the mass and bumper are in contact. M d) x(t) rece B c) Analytically determine the maximum deflection of the bumper, as measured from the point of collision. Analytically determine the time after impact at which the mass separates from the bumper. e) In this idealized one-dimensional problem, what is the steady-state velocity of the mass? f) Use Matlab to plot the displacement x(t) as a function of time from impact to the instant of separation.