A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity.

(a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 12 cos 2t + 3 sin 2t.

(b) Graph the transient and steady-state solutions on the same coordinate axes.

(c) Graph the equation of motion.