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Equation of motion for coupled oscillators

  1. Jul 4, 2012 #1
    Attached is the formula for the equation of motion for a system of coupled oscillators.
    Could someone please tell me what the variables and indices refer to here?
    Thanks!!! :)
     

    Attached Files:

  2. jcsd
  3. Jul 4, 2012 #2

    tiny-tim

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    hi snellslaw! :smile:

    instead of the easy case of the force on an oscillator being proportional to its displacement,

    it's a function of the displacements of itself and another oscillator :wink:
     
  4. Jul 4, 2012 #3
    Thanks TinyTim! So is "a" the spring constant?
     
  5. Jul 5, 2012 #4

    tiny-tim

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    there are n2 a's :confused:
     
  6. Jul 5, 2012 #5

    mps

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    So are the "a"s just constants?
    x is the displacement from equilibrium right?

    Thanks! :)
     
  7. Jul 5, 2012 #6

    tiny-tim

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    yes, the n x's are the n displacements, and the n2 a's are the n2 (or n2/2 if they're symmetric) constants
     
  8. Jul 5, 2012 #7
    The i means you are dealing with a set of equation. a is a coefficient and summation symbol means that each equation has a certain number of terms. For example:

    [itex]\ddot{x_{1}}=a_{11}x_{1}+a_{12}x_{2}+a_{13}x_{3}[/itex]

    [itex]\ddot{x_{2}}=a_{21}x_{1}+a_{22}x_{2}+a_{23}x_{3}[/itex]

    [itex]\ddot{x_{3}}=a_{31}x_{1}+a_{32}x_{2}+a_{33}x_{3}[/itex]

    Where i = 1 to 3 and j = 1 to 3. You have 3 equations with 3 unknown, and can solve this using the matrix determinant method.

    Regards.
     
  9. Jul 5, 2012 #8
    @mps: hey are you preparing for the same thing? :P

    Thanks everyone!
     
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