Equation of motion for coupled oscillators

  • Thread starter snellslaw
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  • #1
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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!!! :)
 

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Answers and Replies

  • #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:
 
  • #3
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Thanks TinyTim! So is "a" the spring constant?
 
  • #4
tiny-tim
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there are n2 a's :confused:
 
  • #5
mps
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So are the "a"s just constants?
x is the displacement from equilibrium right?

Thanks! :)
 
  • #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
 
  • #7
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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.
 
  • #8
16
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@mps: hey are you preparing for the same thing? :P

Thanks everyone!
 

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