A 56 lb weight stretches a spring 14 feet. The weight hangs vertically from the spring and a damping force numerically equal to 27 times the instantaneous velocity acts on the system. The weight is released from 7 feet above the equilibrium position with a downward velocity of 30 ft/s. (a) Determine the time (in seconds) at which the mass passes through the equilibrium position. (b) Find the time (in seconds) at which the mass attains its extreme displacement from the equilibrium position.