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Let's apply the Green's function solution to the case where the oscillator
starts out at rest at the origin, and a constant force F is applied at
time t = 0 and lasts for
a time . The displacement as a function of time for t > 0 is

x(t) = dt'sin([t  t'])
 (17)

with result

x(t) =
 (18)

and we get the expected result that the oscillator oscillates around
the new equilibrium position while the force is applied, and then
oscillates around the origin when the force is released.