Chapter 6.4, Problem 23P

(a)

To determine

The solution of the initial value problem, $y^{″}+y=h\left(t\right),y\left(0\right)=0,y^{\prime }\left(0\right)=0$.

(b)

To determine

To plot: The solution $y\left(t\right)=1-\cos t+2{\displaystyle \sum _{k=1}^n{\left(-1\right)}^k\left(1-\cos \left(t-\frac{11k}{4}\right)\right)u_{11\frac{k}{4}}t}$ for $0\le t\le 90\text{ and }n\ge 33$.

(c)

To determine

To estimate: The slow period and the fast period of the oscillator from the graph obtained in part (b).

(d)

To determine

The slow period and the fast period of the oscillator for the given slow and fast frequency and to compare the results with the results obtained in (c).