A 12-lb weight (mass m = 0.375 slugs in fps units) is attached both to a vertically suspended spring that it stretches 6 in. and to a dashpot that provides 3 lb of resistance for every foot per seconde of velocity.
(a) If the weight is pulled down 1ft below its static equilibrium position and then released from rest at t = 0, find its position function x(t).
(b) Find the frequency, time-varying amplitude, and phase angle of the motion.