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Coupled oscillator question

I've got a question about coupled oscillators - I'm trying to model the motion of a situation where we have three springs and two masses, and the system is horizontal (see attachment for more details). I'm trying to do the most general case possible, i.e. where the moduli and natural lengths of the springs are unknown, as are the masses, lengths and total length etc. I've bumped into a problem - if x and y are the displacements from each mass in equilibrium respectively, then I should end up with 2 equations from Newton's second law - involving only x and y. However, in an attempt at a Newton's second law equation I end up getting a constant term in there that shouldn't be there - could someone tell me where I have gone wrong? I've checked the determinant using Microsoft Mathematics and I'm sure it's right, but I know that this isn't working because I tried putting in some numbers from a past university paper and didn't get the right answer.

Help would be much appreciated! :smile: