Question: 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} ight.)

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

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

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