Chapter 17, Problem 24P

(a)

To determine

Find the Fourier series coefficients $a_2$ and $b_2$ of the periodic function shown in Figure 17.62.

(b)

To determine

Find the magnitude and phase of the component of function $f\left(t\right)$ when ${\omega }_n=10\frac{\text{rad}}{\text{s}}$.

(c)

To determine

Evaluate $f\left(\frac{\pi }{2}\right)$ for the first four nonzero terms.

(d)

To determine

Show that $\frac{\pi }{4}=\frac{1}{1}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\mathrm{...}$