Find the state-space form of the mathematical model. (left{begin{array}{l}ddot{x}_{1}+frac{2}{5}left(x_{1}-x_{3} ight)-frac{3}{5}left(dot{x}_{2}-dot{x}_{1} ight)-frac{1}{2}left(x_{2}-x_{1} ight)=0 ddot{x}_{2}+frac{3}{5}left(dot{x}_{2}-dot{x}_{1} ight)+frac{1}{2}left(x_{2}-x_{1} ight)=F(t)

Find the state-space form of the mathematical model.

\(\left\{\begin{array}{l}\ddot{x}_{1}+\frac{2}{5}\left(x_{1}-x_{3}\right)-\frac{3}{5}\left(\dot{x}_{2}-\dot{x}_{1}\right)-\frac{1}{2}\left(x_{2}-x_{1}\right)=0 \\ \ddot{x}_{2}+\frac{3}{5}\left(\dot{x}_{2}-\dot{x}_{1}\right)+\frac{1}{2}\left(x_{2}-x_{1}\right)=F(t) \\ \dot{x}_{3}=\frac{3}{5}\left(x_{1}-x_{3}\right)\end{array}\right.\), outputs are \(x_{2}\) and \(x_{3}\).