Derive the state-variable equations (in vector form) for the given nonlinear system model. (left{begin{array}{l}ddot{x}_{1}+frac{1}{3}left|dot{x}_{1} ight| dot{x}_{1}=x_{2}^{3} dot{x}_{2}=x_{1}+2 sin tend{array} ight.)

Derive the state-variable equations (in vector form) for the given nonlinear system model.

\(\left\{\begin{array}{l}\ddot{x}_{1}+\frac{1}{3}\left|\dot{x}_{1}\right| \dot{x}_{1}=x_{2}^{3} \\ \dot{x}_{2}=x_{1}+2 \sin t\end{array}\right.\)