# Equation of motion for coupled oscillators

1. Jul 4, 2012

### snellslaw

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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2. Jul 4, 2012

### tiny-tim

hi snellslaw!

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

3. Jul 4, 2012

### snellslaw

Thanks TinyTim! So is "a" the spring constant?

4. Jul 5, 2012

### tiny-tim

there are n2 a's

5. Jul 5, 2012

### mps

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

Thanks! :)

6. Jul 5, 2012

### tiny-tim

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. Jul 5, 2012

### AbigailM

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:

$\ddot{x_{1}}=a_{11}x_{1}+a_{12}x_{2}+a_{13}x_{3}$

$\ddot{x_{2}}=a_{21}x_{1}+a_{22}x_{2}+a_{23}x_{3}$

$\ddot{x_{3}}=a_{31}x_{1}+a_{32}x_{2}+a_{33}x_{3}$

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. Jul 5, 2012

### snellslaw

@mps: hey are you preparing for the same thing? :P

Thanks everyone!