Question: Find a suitable set of state variables, derive the state-variable equations, and form the state equation. (left{begin{array}{l}ddot{x}_{1}+frac{1}{4} dot{x}_{1}+frac{2}{3}left(x_{1}-x_{2} ight)=F_{1}(t) 2 dot{x}_{2}+x_{2}+frac{2}{3}left(x_{2}-x_{1} ight)=F_{2}(t)end{array} ight.)

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

$\left\{\begin{array}{l}\ddot{x}_{1}+\frac{1}{4} \dot{x}_{1}+\frac{2}{3}\left(x_{1}-x_{2}\right)=F_{1}(t) \\ 2 \dot{x}_{2}+x_{2}+\frac{2}{3}\left(x_{2}-x_{1}\right)=F_{2}(t)\end{array}\right.$

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