The body of an automobile is to be protected by a spring-loaded bumper, which is attached to the automobile's frame. Design the bumper so that it will stop a 3500-lb car travelling freely at 5 mi/h and not deform the springs more than 3 in. Submit a sketch of your design showing the placement of the springs and their stiffness. Plot the load-deflection diagram for the bumper during a direct collision with a rigid wall, and also plot the deceleration of the car as a function of the spring's displacement