The angular equation of motion of the pendulum is given by Newton's equation and with no external force it reads $$\begin{equation} ml\frac{d^2\theta}{dt^2}+mgsin(\theta)=0, \tag{44} \end{equation}$$ with an angular velocity and acceleration given by $$\begin{equation} v=l\frac{d\theta}{dt}, \tag{45} \end{equation}$$ and $$\begin{equation} a=l\frac{d^2\theta}{dt^2}. \tag{46} \end{equation}$$