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

\(\left\{\begin{array}{l}2 \ddot{x}_{1}+4 \dot{x}_{1}-2 \dot{x}_{2}+x_{1}-x_{2}=F_{1}(t) \\ \ddot{x}_{2}-2 \dot{x}_{1}+2 \dot{x}_{2}-x_{1}+x_{2}=F_{2}(t)\end{array}\right.\)