Consider again the system in Example 1 of this section, in

Chapter 6, Problem 13

(choose chapter or problem)

Consider again the system in Example 1 of this section, in which an oscillation is excited by a unit impulse at t = 5. Suppose that it is desired to bring the system to rest again after exactly one cyclethat is, when the response first returns to equilibrium moving in the positive direction. (a) Determine the impulse k(t t0) that should be applied to the system in order to accomplish this objective. Note that k is the magnitude of the impulse and t0 is the time of its application. (b) Solve the resulting initial value problem, and plot its solution to confirm that it behaves in the specified manner.