Let
f(x)=2−x 0≤x≤2, 2+x −2≤x≤0.
a. Compute the Fourier coefficients of f(x) for −2 ≤ x ≤ 2.
b. Solve the initial-boundary value problem,
utt= 4uxx, 0≤x≤2,
u(0,t)=0, u(2,t)=0,
u(x,0)=f(x),
ut(x,0)=0
Express the solution as a Fourier series.

Question

Let
f(x)=2−x	0≤x≤2, 2+x −2≤x≤0.
a. Compute the Fourier coefficients of f(x) for −2 ≤ x ≤ 2. 
b. Solve the initial-boundary value problem,
utt= 4uxx, 0≤x≤2,
u(0,t)=0, u(2,t)=0,
u(x,0)=f(x),
ut(x,0)=0
Express the solution as a Fourier series.

anonymous · Answer

derivate f(x)
then the function will be in constant so could be easily integrable with e^-jkwt.

after wards multiply the answer with 1/-jwk

anonymous · Answer

I don't think so. The question asked for Fourier coefficient.

anonymous · Answer

derivative in t domain equals multiplying with 1/-jwk in k domain