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Normal modes problem

  1. Oct 19, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle P of mass 3m is suspended from a fixed point O by a massless linear spring with strength alpha. A second particle Q of mass 2m is in turn suspended from P by a second spring of the same strength. The system moves in the vertical straight lie through O . Find the normal frequencies and the form of the normal modes for this system. Write down the form of the general motion.

    2. Relevant equations



    3. The attempt at a solution

    3mx''= -alpha*x+alpha*(y-x)

    2my''= -alpha*(y-x)

    dividing out m, my set of equations looks like:

    3x''+2xn^2-yn^2=0

    2y''+yn^2+xn^2=0
    n^2=alpha/m
    Let x=A cos(omega*t-gamma) and y= B cos(omega*t-gamma)

    x''=-A*omega^2*cos(omega*t-gamma)
    y''=-B*omega^2*cos(omega*t-gamma)

    plugging x'' and y'' into two equations I get:

    3(-A*omega^2)+2(A)n^2-(B)n^2=0
    2(-B*omega^2])+Bn^2+ An^2=0

    -omega^2*n^2+n^4=0

    There is something wrong with how I set up my equations and I cannot spot my errors.
     
    Last edited: Oct 19, 2008
  2. jcsd
  3. Oct 19, 2008 #2
    anyone having trouble reading my problem?
     
  4. Oct 19, 2008 #3
    Yeah I think you should rewrite it in LaTeX, I had a hard time trying to read it. I guess x(double dot) means second derivative of x? You should definitely retype it though, makes it easier for anyone who can help you.
     
  5. Oct 19, 2008 #4
    I edited my OP. Are you able to read it any better?
     
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