A mass of 1 slug stretches a spring 2ft and comes to rest at equilibrium. The system is attached to a dashpot that imparts a damping force equal to eight times the instantaneous velocity of the mass. Find the equation of motion if an external force equal to f(t) = 8 sin(4t) is applied to the system beginning at time t = 0. What is the transient solution? What is the steady-state solution?

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