I’m looking for the lagrangian function of the following problem (as seen in the picture). We have a mass connected to two springs. We can deglect the mass in two dimensions.

My main problems are:

1. What coordinats should I use?
2. How can I define the potential energy of the springs in regard of the mass?

In Newtonian mechanics, the approach is clear. I use polar-like coordinates and obtain a 2D-vector field resulting in two coupled ode’s.

I assume the potential energy is way easier than I think. Probably something like (in Cartesian coordinates):

$$ V = \frac{1}{2} k \left( x^2 + y^2 \right) $$

But isn’t that the potential energy for a setup with two additional vertical springs? Somehow I can't wrap my head around this. I would very much appreciate your help!

Thanks in advanced!

I’m looking for the lagrangian function of the following problem (as seen in the picture). We have a mass connected to two springs. We can deglect the mass in two dimensions.

My main problems are:

1. What coordinates should I use?

2. How can I define the potential energy of the springs in regard of the mass?

In Newtonian mechanics, the approach is clear. I use polar-like coordinates and obtain a 2D-vector field resulting in two coupled ode’s.

I assume the potential energy is way easier than I think. Probably something like (in Cartesian coordinates):

$$ V = \frac{1}{2} k \left( x^2 + y^2 \right) $$

But isn’t that the potential energy for a setup with two additional vertical springs? Somehow I can't wrap my head around this. I would very much appreciate your help!