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One Mass, Two Springs, 2-D Motion

  1. Feb 10, 2009 #1
    1. The problem statement, all variables and given/known data

    A mass M is confined to move on a smooth, flat, two-dimensional surface. Label the locations on this surface using the Cartesian coordinates (x,y). The mass is attached to two identical springs, each of length l and spring constant k. One spring has one end fixed to the point (-L, 0) and the other spring has one end fixed to the point (L, 0)

    1) Find the normal modes of this system when l<L.
    2) At t=0, the mass is released at rest from the point (0.1L, -0.2L). What is the position of the mass for all subsequent times?

    2. Relevant equations

    3. The attempt at a solution

    I used the Lagrangian method to find the equations of motion (see attachment). I'm sure there is something I could do to simplify these two equations by making some sort of approximation. But I'm not sure what to do. Any help would be appreciated. Thanks!
     

    Attached Files:

    • DEs.png
      DEs.png
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      18.5 KB
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  2. jcsd
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