A bumper, consisting of a nest of three springs, is used to arrest the horizontal motion of

Question:

A bumper, consisting of a nest of three springs, is used to arrest the horizontal motion of a large mass which is traveling at 40 ft/sec as it contacts the bumper. The two outer springs cause a deceleration proportional to the spring deformation. The center spring increases the deceleration rate when the compression exceeds 6 in. as shown on the graph. Determine the maximum compression x of the outer springs.