I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to derive the $x$ and $y$ components of acceleration. The formula I have derived is the following: $$\ddot θ = -(g/l)\sinθ$$
And the $x$ and $y$ are these: $$x = l\sinθ$$ $$y = l(1-\cosθ)$$
So now I'm not sure what to do next... Do I use the chain rule and differentiate $x$ and $y$ with respect to time twice? I don't really know what to do here...
If you can, please give me a hint instead of a full solution, and, if possible, stick to these formulas and Euler-Lagrange equations, instead of a solution that would incorporate something not directly related.