A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb · s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 6 in/s, find its position u at any time t. (Use g = 32 ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)a) u(t) =b) Plot u versus t. c) Determine when the mass first returns to its equilibrium position. (Round your answer to four decimal places.)d) Find the time ? such that |u(t)| < 0.01 inches for all t > ?. (Round your answer to four decimal places.)