1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Where Did I Go Wrong In Solving This PDE?

  1. Mar 30, 2008 #1
    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.

    Attached Files:

  2. jcsd
  3. Mar 30, 2008 #2
  4. Mar 30, 2008 #3
    Have you tried to read the thumbnails, ColdFusion85. The quality is poor.
  5. Mar 30, 2008 #4
    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.
  6. Mar 30, 2008 #5
    unless you have a mac and then you use SHIFT +
  7. Mar 31, 2008 #6
    Looking for help again. Can anyone figure out what's wrong?
  8. Mar 31, 2008 #7
    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: Mar 31, 2008
  9. Mar 31, 2008 #8
    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?
  10. Mar 31, 2008 #9


    User Avatar
    Science Advisor

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook