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Coupled Vertical Oscillators with Gravity

  1. Apr 25, 2007 #1
    Hey, I'm just having some trouble getting started with this problem.

    -------------
    (
    )
    (
    m1
    (
    )
    (
    2m1
    Crude representation: (The parantheses are supposed to be the springs)

    There is a mass (m1) that is attached vertically to a board by a spring of spring constant k and length b. There is a second mass (2m1) attached by an identical spring to the first mass.

    I'm supposed to find the normal frequencies in a constant (so it isn't affected by x1 and x2, right?) gravitational field and the normal coordinates. I can do coupled oscillators pretty easily, but I'm just having a hard time setting it up.

    Best guess...
    m1x1'' = -k1x1 +k2(x2-x1) + g
    m2x2'' = k2x2 + g

    I guess I'm not exactly sure where g goes into the MX''=-Kx matrix.
     
    Last edited: Apr 25, 2007
  2. jcsd
  3. Apr 26, 2007 #2

    nrqed

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    Just shift x_2. It's easy to get a shifted x_2 that will get rid of the g in both equations. Than you can solve the usual way and in the final solution you can go back to the original x_2
     
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