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Forced Normal mode frequencies of 4 horizontal springs, 3 masses

  1. Apr 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey guys.
    The title says it all pretty much. We need to find the normal mode frequencies of a driven/forced system containing 3 equal masses connected by 4 springs of equal spring constant k.

    2. Relevant equations
    [itex]F=m\ddot{x}[/itex]
    Spring potential
    [itex]V = 0.5kx^{2}[/itex]
    Force-potential relationship
    [itex]F = -\frac{dV}{dx}[/itex]
    Natural frequency of the system
    [itex]ω_{0}^{2} = \frac{k}{m}[/itex]

    3. The attempt at a solution
    So, I'm gona type this up in word and show you guys what I've done. Obviously there are 3 masses, so we expect 3 normal mode frequencies. I've found two, I dont know how to get the third one.
    https://imageshack.us/scaled/large/818/normalmodefrequencyques.jpg [Broken]
    Thanks again guys.
     

    Attached Files:

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 19, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    I haven't checked all the steps in detail. But, after you expanded your determinant, it looks like you have an overall factor of ##(2\omega_0^2-\omega^2)##. You then divided out this overall factor. I think that's where you lost your 3rd solution.
     
  4. Apr 19, 2013 #3
    Yea, you're right...that's it. Thanks a lot man :)
     
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