Euler Lagrange equations with viscous dissipation

[Dustinsfl]

Homework Statement

The system can pivot at point O and I am taking small angle approximations.
I am trying to determine the Lagrangian, $\mathcal{L} = T - U$ for the following system:

Homework Equations

E-L equation with dissipation: $\frac{\partial\mathcal{L}}{\partial q_i} - \frac{d}{dt}\frac{\partial\mathcal{L}}{\partial\dot{q}_i} + \frac{\partial D}{\partial\dot{q}_j} = 0$

The Attempt at a Solution

I am going to use the generalized coordinate theta.

For the circular mass, I have the potential energy to be $mg(1-\cos(\theta)) = \frac{mg\theta^2}{2}$ and the kinetic energy is $\frac{1}{2}J\dot{\theta}^2$ where J is the mass moment of inertia. The potential energy of the spring is $\frac{1}{2}kx^2$, and the dissipative energy is $D = c\frac{\dot{x}^2}{2}$.

Before I convert the xs to thetas am I missing a kinetic or potential energy?

 

[BvU]

Don't think you are missing anything. I do worry about the potential energy signs.