3. Consider again the system in Example 1 of this section, in which an oscillation is

Chapter 6, Problem 13

(choose chapter or problem)

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