How do you find angular frequencies in coupled masses using Hooke's Law?

[The-Exiled]

Homework Statement

There are 3 masses connected by springs of the same spring constant (k). The end masses are connected to solid walls via 2 more springs. Assuming simple harmonic motion find the angular frequencies (\omega) for each of the normal modes of vibrations...

Homework Equations

The Attempt at a Solution

I just need help getting the equations of motion for each of the masses, I can't seem to get them right

 

[hikaru1221]

What have you got so far? Posting your work may assist everyone in spotting out your mistake

 

[The-Exiled]

So far I have got:

Mass A:

ma_{A} + kx_{B} - kx_{C} = 0

Mass B:

ma_{B} + kx_{A} - 2kx_{B} + kx_{C} = 0

Mass C:

ma_{C} + kx_{A} - kx_{B} + 2kx_{C} = 0

Thats the best I can do... :S

Sorry, the superscripts are meant to be subscripts XD

 

[hikaru1221]

Could you please describe or draw the system? I cannot deduce any system that matches your equations.

 

[The-Exiled]

hey, sorry for not putting up a diagram. didn't think to do that XD

It's okay though, I worked it out finally.

Thanks for trying to help :)