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Where Did I Go Wrong In Solving This PDE?

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It is a 1-D wave equation problem with fixed ends, no initial velocity, and initial displacement of [tex]2sin(\pi x)[/tex] on the interval 0<x<4, t>0.

See my attached documents of my work. I end up with a c_n value of 0 based on the integration. I am pretty confident I set up the problem correctly as it follows a similar, generalized problem in my class notes. Obviously I used actual numbers in this problem. Can anyone spot any errors in my work? Thanks for your help.
 

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Answers and Replies

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Anyone?
 
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Have you tried to read the thumbnails, ColdFusion85. The quality is poor.
 
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No they aren't. Place your cursor over the picture, the magnifying glass appears. Just click and you will be able to see it fine.
 
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unless you have a mac and then you use SHIFT +
 
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Looking for help again. Can anyone figure out what's wrong?
 
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Try moving this thread to the section Differential Equations...looks like thats what this is. You'll probably have a higher chance of getting help there.
 
Last edited:
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At the end of your first page, knowing that [itex] \sqrt{\lambda} = \frac{n \pi}{4} [/itex] you went from
[tex] T^{\prime \prime} - 9 \lambda T = 0 \text{ to } T^{\prime \prime} + \frac{9 n^2 \pi ^2}{16} T = 0[/tex].
Why'd you switch sign?
 
HallsofIvy
Science Advisor
Homework Helper
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You have
[tex]\sum C_n Sin(\frac{n\pi x}{4})= 2 Sin(\pi x)[/tex]
for the initial value and then start calculating a complicated Fourier coefficient.

Isn't it obvious that if C4= 2, all other Cn= 0 satisfies that? Since the sines are "orthogonal", your integral should have been 0 for all n except n= 4. You don't need the full sine series when your function is a single sine!
 

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