- #1
Fourier mn
Homework Statement
String of length L and string mass-density of[tex]\mu[/tex] is fixed at both ends. at t=0
y(x,t)=
4xh/L 0<x<L/4
2h-4xh/L L/4<x<L/2
0 L/2<x<0
Find the first four coefficients, is anyone of them is zero? If so why is it?
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the peak is L/4 and the right corner of the triangle is L/2.
Homework Equations
2/L{[tex]\int[/tex](4xh/L) sin(nx[tex]\pi[/tex]/L) over 0<x<L/4 +
[tex]\int[/tex](2h-4xh/L)sin(nx[tex]\pi[/tex]/L) over L/4<x<L/2 +
[tex]\int[/tex] 0*sin(nx[tex]\pi[/tex]/L) over L/2<x<L}
The Attempt at a Solution
so the third integral is equal to zero, we are left with only two.
After integrating the first two I've got the following result for An=
(8h)/(n[tex]\pi[/tex])^2[2sin(n[tex]\pi[/tex]/4)-sin(n[tex]\pi[/tex]/2)]
is this result correct? I've never seen Fourier series described by two sine terms. should I change the height to (h+1) so the last integral won't be zero and then integrate?
any other ideas how to go about it?