Decide whether the system in Problem 4 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 Problem4:

\(\left\{\begin{array}{l}\ddot{x}+\frac{2}{5} \dot{x}+x=2 y \\ 2 \dot{y}+\frac{1}{2} y+x=F(t)\end{array}\right.\)