The block, having a weight of 15 lb, is immersed in a liquid such that the damping force a...

The block, having a weight of 15 lb, is immersed in a liquid such that the damping force acting on the block has a magnitude of F = (0.8|v|) lb, where v is the velocity of the block in ft/s. If the block is pulled down 0.8 ft and released from rest, determine the position of the block as a function of time. The spring has a stiffness of k = 40 lb/ft. Consider positive displacement to be downward.