A friend of mine came up with this system of ODEs :
$$g \cos \theta - \frac{C}{1 - \sin \theta} \frac{d^{2}x}{dt^{2}} = \frac{d^{2}x}{dt^{2}} (1 - \sin \theta) - (x - R (\theta - \theta_{0})) \left( \frac{d \theta}{dt} \right)^{2} \\ - g \sin \theta = (x - R (\theta - \theta_{0})) \frac{d^{2}\theta}{dt^{2}} + 2 \frac{dx}{dt} \frac{d \theta}{dt} - R \left( \frac{d \theta}{dt} \right)^{2} - \frac{d^{2}x}{dt^{2}} \cos \theta$$
($x(t)$ and $\theta(t)$ are the desired functions and the rest are all constants.)
I have tried it on Mathematica but it seems the derivative diverges at all values of $t$. Can anyone help?