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## Homework Statement

One mass [itex]m[/itex] constrained to the x-axis, another mass [itex]m[/itex] constrained to the y-axis. Each mass has a spring connecting it to the origin with elastic constant [itex]k[/itex] and they are connected together by elastic constant [itex]c[/itex]. I.e. we have a right-angle triangle made from the springs with lengths [itex]b[/itex], [itex]b[/itex], and [itex]\sqrt{2} b[/itex].

Write the Lagrangian, find the normal mode frequencies.

## The Attempt at a Solution

Again having trouble with the coupling. For the two springs connected to the origin the potentials are straightforward:

[tex]V = \frac{1}{2} k x^2 + \frac{1}{2} k y^2[/tex]

Given the geometry wouldn't the coupling spring add the potential,

[tex]V = \frac{1}{2} c \left [ \sqrt{x^2 + y^2} - \sqrt{2} b \right ]^2 = \frac{1}{2} c \left [ x^2 + y^2 - 2 \sqrt{2 x^2 + 2 y^2} + 2 b^2 \right ][/tex]

But I don't know how to put this in matrix form...

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