A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 8 sin(4t) is applied to the system.(In this scenario, the mass is initially at rest in the equilibrium position). Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity).
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