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Finding Normal Modes (completely stumped)

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Two horizontal frictionless rails make an angle θ with eachother. Each rail has a bead of mass m on it and the beads are connected by a spring with spring constant k and relaxed length=zero.Assume that one of the rails is positioned a tiny distance above the other so that the beads can pass freely though the crossing. Find the Normal Modes.

    2. Relevant equations
    the only force involved is the spring force so:
    Fs=-k(Δx)=ma
    where Δx=x1sin(θ/2)+x2sin(θ/2)

    3. The attempt at a solution

    so for each bead (x1,x2):

    a1+(k/m)(x1sin(θ/2)+x2sin(θ/2))=0
    a2-(k/m)(x1sin(θ/2)+x2sin(θ/2))=0

    I guess x1=Ae(iwt) and x2=Be(iwt) and get this:

    -Aw^2 +(ksin(θ/2)/m)(A+B)=0
    -Bw^2 -(ksin(θ/2)/m)(A+B)=0

    Did I set up the equation incorrectly? Finding Normal Modes generally confuses me and this is about as far as I can get, help appreciated!
     
    Last edited: Nov 18, 2012
  2. jcsd
  3. Nov 19, 2012 #2
    Aren't there just two modes. X_1 = X_2 and X_1 = - X_2 ??

    They both move together or they both move in oppositely?
     
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