Engineering Board Exam Reviewer · Fourier Series · medium

The square wave f(x)=-1 on (-π,0) and f(x)=1 on (0,π) has Fourier coefficients bn. Find b3.

1. 0.424
2. 1.273
3. 0.212
4. 0.141

Answer

A. 0.424

Solution

bn=1/π -ππf(x) nx,dx= 2π 0π nx,dx=2(1- nπ)/nπ. For n=3: b3=4/3π 0.424.

More Fourier Series questions

1. Find b3 in the Fourier series of f(x)=x on (-π,π).
2. Which Fourier coefficients vanish for the odd function f(x)=x on (-π,π)?
3. The Fourier series of f(x)=x2 on (-π,π) is π2/3+4 n=1∞(-1)n/n2 nx. Evaluate it at x=π to find n=1∞ 1n2.
4. The half-range sine series of f(x)=x on (0,2) is bn π x/2. Find b2.
5. The square wave f(x)=-1 on (-π,0) and f(x)=1 on (0,π) has a jump at x=0. To what value does its Fourier series converge at x=0?
6. Find a1 in the Fourier series of f(x)=|x| on (-π,π).
7. Find the constant term a0/2 of the Fourier series of f(x)=x2 on (-π,π).

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