Find the transfer function $G(s)=\frac{x_3(s)}{F(s)}($Note: The required equations are explicitly indicated in the comment lines of the code, please write in the correct format$).$

Input : ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(t)$; output: $x_3(t)$ obtain the state space model of the system $($with $6$ state variables, including positions and their derivatives,

$($:$x_1=x_1,x_2=x_2,x_3=x_3,x_4=x_1^{},x_5=x_2^{},x_6=x_3^{}$