Find the second harmonic of the function $h(x)=$$\left\{\begin{array}{c}
2 \pi \
0
\end{array}\right.$$\begin{aligned}
-\pi

Question

Find the second harmonic of the function $h(x)=$$\left\{\begin{array}{c}
2 \pi \
0
\end{array}\right.$$\begin{aligned}
-\pi< \
0<
\end{aligned}$$\begin{array}{l}
x \leq 0 \
x \leq \pi
\end{array}$ .
A) $\frac{4}{3} \sin 3 x$
B) $-\frac{4}{3} \sin 3 x$
C) $\frac{2}{3} \sin 3 x$
D) $-\frac{2}{3} \sin 3 x$
E)0

Quizplus · Accepted Answer

The given function $h(x)$ is a piecewise constant function with a value of $2\pi$ for $-\pi < x \leq 0$ and $0$ for $0 < x \leq \pi$. The second harmonic of a function refers to a component of its Fourier series that oscillates at twice the fundamental frequency. However, since the function is constant in each interval, its Fourier series representation will not include sine terms for harmonics, including the second harmonic. Thus, the correct answer is that the second harmonic is $0$, indicating that there is no component of the function that oscillates at twice the fundamental frequency.

Find the Second Harmonic of the Function h(x)=h(x)=h(x)= {2π0\left\{\begin{array}{c}2 \pi \\0\end{array}\right.{2π0​

Find the Second Harmonic of the Function $h(x)=$ $\left\{\begin{array}{c}2 \pi \\0\end{array}\right.$