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: 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.


    2. Relevant equations

    b_n = 0 because released from rest

    3. The attempt at a solution



    Attached Files:

  2. jcsd
  3. Nov 23, 2015 #2


    User Avatar
    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)##
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted