Aspring 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 2 cos 2t lb. (use g = 32 ft/s2 for the acceleration due to gravity. let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t ) 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.