Find a suitable set of state variables, derive the state-variable equations, and form the state equation. (left{begin{array}{l}m L_{1}^{2} ddot{theta}_{1}+left(m g L_{1}+k L_{2}^{2} ight) theta_{1}-k L_{2}^{2}

Find a suitable set of state variables, derive the state-variable equations, and form the state equation.

\(\left\{\begin{array}{l}m L_{1}^{2} \ddot{\theta}_{1}+\left(m g L_{1}+k L_{2}^{2}\right) \theta_{1}-k L_{2}^{2} \theta_{2}=0 \\ m L_{1}^{2} \ddot{\theta}_{2}+\left(m g L_{1}+k L_{2}^{2}\right) \theta_{2}-k L_{2}^{2} \theta_{1}=0\end{array} \quad \quad m, k, g, L_{1}, L_{2}=\right.\) const