The cannon fires a 10-lb cannonball with an absolute velocity of 800 ft/sec at 20° to th...

The cannon fires a 10-lb cannonball with an absolute velocity of 800 ft/sec at 20^° to the horizontal. The combined weight of the cannon and its cart is 1610 lb. If the recoil mechanism consists of the spring of constant k=150 lb/in. and the damper with viscous coefficient c=600 lb-sec/ft, determine the maximum recoil deflection x_max of the cannon unit.