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How do I find the normal modes of massless string w/ masses?

  1. Oct 25, 2015 #1
    1. The problem statement, all variables and given/known data
    So, a string with length L and a mass of M is given tension T. Find the frequencies of the smallest three modes of transverse motion. Then compare with a massless string with the same tension and length, but there are 3 masses of M/3 equally spaced. So this is problem #1
    http://www.physics.purdue.edu/~jones105/phys42200_Spring2013/Assignment_5_Spring2013.pdf

    2. Relevant equations
    ν * λ = velocity
    velocity = sqrt(T * L / M)
    νn = nν1 n = 1, 2, 3
    ν1 = √(T/(4ML))

    3. The attempt at a solution
    I tried using coupled oscillators and the equation for finding the frequencies.
    ωq=2ω0|sin(q/2)|
    q = nπ/(N+1) where n is the index and N is the number of particles
    This does not give me the correct answer.
    The correct answer is: .84ν1, 1.55ν1, and 2.04ν1.
     
    Last edited: Oct 25, 2015
  2. jcsd
  3. Oct 25, 2015 #2

    TSny

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    Hello. Welcome to PF!

    What did you use for ωo?
     
  4. Oct 25, 2015 #3
    ω02 = T/((M/3)(L/4))
     
  5. Oct 25, 2015 #4

    TSny

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    OK. That should give the correct answer. You'll have to show your detailed calculations in order to find the mistake.
     
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