Find the state-space form of the mathematical model. (left{begin{array}{l}ddot{x}_{1}+3 dot{x}_{1}+frac{3}{2}left(x_{1}-x_{2} ight)=0 2 dot{x}_{2}+x_{2}-frac{3}{2}left(x_{1}-x_{2} ight)=F(t)end{array} ight.), outputs

Find the state-space form of the mathematical model.

\(\left\{\begin{array}{l}\ddot{x}_{1}+3 \dot{x}_{1}+\frac{3}{2}\left(x_{1}-x_{2}\right)=0 \\ 2 \dot{x}_{2}+x_{2}-\frac{3}{2}\left(x_{1}-x_{2}\right)=F(t)\end{array}\right.\), outputs are \(x_{1}\) and \(\dot{x}_{1}\).