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For a string with fixed ends, which normal modes are missing?

  1. Nov 22, 2015 #1
    1. The problem statement, all variables and given/known data

    Here's the problem. I was able to find the a_n and b_n values, my question is mainly on part (c), how do I find which modes are missing? The function is odd, so even modes should disappear, but cos(n*pi) doesn't disappear, it's either +1 or -1. I'd greatly appreciate any help.

    upload_2015-11-22_12-58-32.png



    2. Relevant equations

    upload_2015-11-22_12-57-15.png
    b_n = 0 because released from rest



    3. The attempt at a solution

    upload_2015-11-22_13-1-13.png

    upload_2015-11-22_13-13-11.png
     

    Attached Files:

  2. jcsd
  3. Nov 23, 2015 #2

    RUber

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    Homework Helper

    When it says fixed ends, are we to assume that at x = 0 and x = L, the ends are fixed at ##\xi(0,t) = \xi(L,t) = 0##?
    If so, then you should be able to say something about ##\xi( L/2,t)##.

    Using your equation for a_n, break that into two integrals, one from 0 to L/2 and one from L/2 to L. Then enforce an appropriate matching condition for ##\xi(L/2,t) ## and ##\xi_t(L/2,t)##
     
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