A dynamic system model is derived as [left{begin{array}{l} 4 ddot{x}_{1}-dot{x}_{1}-3 x_{1}+x_{2}=f(t) dot{x}_{2}+frac{1}{3} x_{1}+2 x_{2}=0 end{array} ight.]

A dynamic system model is derived as

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

where the input is \(f\) and the outputs are \(x_{2}\) and \(\dot{x}_{1}\).

a. Find the state-space form.

b. Derive the state-space form of the decoupled system.