A spring is stretched 6 in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb·s/ft and is acted on by an external force of 4 cos 2t lb.

a) Determine the steady state response of this system.

b) If the given mass is replaced by a mass m, determine the value of m for which the amplitude of the steady state response is maximum.