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) = 2 sin(4t)
is applied to the system. 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.)