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 3 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) = 8 cos 2t + 2 sin 2t.