Decide whether the system in Problem 5 is stable. A linear dynamic system is stable if the homogeneous solution of its mathematical model, subjected to the prescribed initial conditions, decays. More practically, a linear system is stable if all the eigenvalues of its state matrix have negative real parts; that is, they all lie in the left half plane.

Data From  Problem 5:

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