Rod AB has weight W and is attached to two smooth collars at its ends by ball-and-socket joints. If collar A is moving downward with speed v_A when z = a, determine the speed of A at the instant z = 0. The spring has unstretched length c. Neglect the mass of the collars. Assume the angular velocity of rod AB is perpendicular to its axis.

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Given: W = 6 lb VA = 8 ft a = 3 ft b = 6 ft c = 2 ft k = 4 S lb ft 8 = 2 ft B