Chapter 5.7, Problem 13P

Consider again the system in Example 3 of this section, in which an oscillation is excited by a unit impulse at $t=5$. suppose that it is desired to bering the sytem of rest again after exactly one cycle –that is, when the reponse the first returns to equilibrium moving in the positive direction.

a) Determine the impulse $k\delta (t-t_0)$ that should be applied to the system in order to accomplish this objective. Note that $-k$ is the magnitude of the impulse and $t_0$ is the time of ots application.

b) Solve the resulting initial value problem and plot its solution to confirm that it behaves in the specified manner.