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Normal Modes - 2 springs question

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data

    jtnrd4.png


    2. Relevant equations



    3. The attempt at a solution

    When i do the matrix multiplication of the 2x2 and 2x1 matrix, I get 2 conflicting solutions that don't match at all! So which one do i take to find ratio of X and Y?

    14lo94m.png
     
  2. jcsd
  3. Jan 24, 2013 #2

    TSny

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    Are you sure they don't match? What 2 conflicting solutions did you get for the ratio X/Y?
     
  4. Jan 27, 2013 #3
    Well it's pretty obvious when it is expanded... the top entry gives something like:

    (k/m)Y = (1-√5)(K/2m)X

    while the bottom entry gives:

    (k/m)X = -(1+√5)(K/2m)Y
     
  5. Jan 27, 2013 #4

    vela

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    Did you notice that ##(\sqrt{5}-1)(\sqrt{5}+1)=4##?
     
  6. Jan 28, 2013 #5
    Oh I see it now, thank you!
     
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