Assuming general initial conditions, express the system model in

a. Configuration form.

b. Standard, second-order matrix form.

\(\left\{\begin{array}{l}m \ddot{x}_{1}+k x_{1}-\frac{1}{2} k\left(x_{2}-x_{1}\right)-2 c\left(\dot{x}_{2}-\dot{x}_{1}\right)=F_{1}(t) \\ m \ddot{x}_{2}-\frac{2}{3} k\left(x_{3}-x_{2}\right)+\frac{1}{2} k\left(x_{2}-x_{1}\right)+2 c\left(\dot{x}_{2}-\dot{x}_{1}\right)=0 \\ 2 m \ddot{x}_{3}+k x_{3}+\frac{2}{3} k\left(x_{3}-x_{2}\right)+c \dot{x}_{3}=F_{2}(t)\end{array}\right.\)