Find all possible I/O equations. (left{begin{array}{l}ddot{x}_{1}+x_{1}-x_{3}-left(dot{x}_{2}-dot{x}_{1} ight)-frac{1}{2}left(x_{2}-x_{1} ight)=f(t) ddot{x}_{2}+dot{x}_{2}-dot{x}_{1}+frac{1}{2}left(x_{2}-x_{1} ight)=0 dot{x}_{3}=x_{1}-x_{3}end{array}, f(t)= ight.) input, (x_{2},

Find all possible I/O equations.

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