It is shown in mechanics of materials that the stiffness of an elastic cable is k = AE/L where A is the cross sectional area of the cable, E is the modulus of elasticity and L is the length of the cable. A winch is lowering a 4000-lb piece of machinery using at a constant speed of 3ft/s when the winch suddenly stops. Knowing that the steel cable has a diameter of 0.4 in., E = 29 x 106 lb/in2, and when the winch stops L = 30 ft, determine the maximum downward displacement of the piece of machinery from the point it was when the winch stopped.

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30 ft 3 ft/s