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 second of velocity.

(a) If the weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t = 0, find its position function x(t).

(b) Find the frequency, time-varying amplitude, and phase angle of the motion.