Huygen's Swinging Clock Synchronization Simulation

\[ \begin{aligned} \ddot{x} &= \frac{mL\sum_{i=1}^3(\omega_i^2\sin(\theta_i) + g\sin(\theta_i)\cos(\theta_i))}{M+3m+m\sum_{i=1}^3\cos^2(\theta_i)} \\ \\ \ddot{\theta_1} &= \frac{-g\sin(\theta_1) - \ddot{x}\cos(\theta_1)}{L}\\ \\ \ddot{\theta_2} &= \frac{-g\sin(\theta_2) - \ddot{x}\cos(\theta_2)}{L}\\ \\ \ddot{\theta_3} &= \frac{-g\sin(\theta_3) - \ddot{x}\cos(\theta_3)}{L}\\ \end{aligned} \]