2. From free-body and kinetic diagrams, determine the differential equation describ- ing x(t) for the time...

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2. From free-body and kinetic diagrams, determine the differential equation describ- ing x(t) for the time during which the mass is in contact with the bumper plate. 3. From new free-body and kinetic diagrams, determine the differential equation describing (t) for the time during which the mass is not in contact with the bumper plate. 4. Solve the equation from part 2 analytically to find x(t), the displacement of the bumper plate, after the collision occurs but while the mass remains in contact with the bumper plate. Note: during this time, x(t) is also the displacement of the mass. Assume that after the collision, the bumper and mass move together with the same initial velocity of the mass. 5. Use your solution from part 4 to analytically determine the time after collision, tr, at which the mass releases contact with the bumper plate. The free-body diagram of the bumper plate may be helpful in determining the condition(s) under which the mass loses contact with the bumper plate. 6. Use your solution from parts 3 and 5 to analytically find x(t), the displacement of the bumper plate, after the mass loses contact with the bumper plate. 7. Use MATLAB to plot the displacement x(t) as a function of time. Indicate on the plot the time at which the mass loses contact with the bumper. Consider Figure 3.1, which depicts a mass M with the velocity Vo = 1 [m/s] on its way to collide with a bumper. The bumper consists of plate of negligible mass, a spring, and a damper. Use M = 1000 [kg], K = 9850 [N/m] and B = 12500 [N-8/m]. x(t) Leee K M B Figure 3.1: Mass, M, traveling toward a bumper, B & K, with a velocity Vo. 2. From free-body and kinetic diagrams, determine the differential equation describ- ing x(t) for the time during which the mass is in contact with the bumper plate. 3. From new free-body and kinetic diagrams, determine the differential equation describing (t) for the time during which the mass is not in contact with the bumper plate. 4. Solve the equation from part 2 analytically to find x(t), the displacement of the bumper plate, after the collision occurs but while the mass remains in contact with the bumper plate. Note: during this time, x(t) is also the displacement of the mass. Assume that after the collision, the bumper and mass move together with the same initial velocity of the mass. 5. Use your solution from part 4 to analytically determine the time after collision, tr, at which the mass releases contact with the bumper plate. The free-body diagram of the bumper plate may be helpful in determining the condition(s) under which the mass loses contact with the bumper plate. 6. Use your solution from parts 3 and 5 to analytically find x(t), the displacement of the bumper plate, after the mass loses contact with the bumper plate. 7. Use MATLAB to plot the displacement x(t) as a function of time. Indicate on the plot the time at which the mass loses contact with the bumper. Consider Figure 3.1, which depicts a mass M with the velocity Vo = 1 [m/s] on its way to collide with a bumper. The bumper consists of plate of negligible mass, a spring, and a damper. Use M = 1000 [kg], K = 9850 [N/m] and B = 12500 [N-8/m]. x(t) Leee K M B Figure 3.1: Mass, M, traveling toward a bumper, B & K, with a velocity Vo.