A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially releas

Question

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from rest at a point 3 feet above the equilibrium position, and the subsequent motion takes place in a medium that gives a damping force numerically equal to the instantaneous velocity. Find the equation of motion if the mass is driven by an external force f(t) = 5sin2t

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Explanation / Answer

=> mg = kx.....m = 8 pounds , x = 1 foot Find k now , f(t) = ma + V + kx = 5sin2t v = dx/dt a = d^2x / dt^2 => m*d^2x/dt^2 + dx/dt + kx = 5sin2t Solve for x

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