Question: Consider the following system x, =-x, + Ex,(x+x)sin(x +x) *, =x, + Ex,(x +x)sin(x; +x) a) Show that the origin is an equilibrium point

Consider the following system x, =-x, + Ex,(x+x)sin(x +x) *, =x, +

Consider the following system x, =-x, + Ex,(x+x)sin(x +x) *, =x, + Ex,(x +x)sin(x; +x) a) Show that the origin is an equilibrium point of the system. b) Linearize the system about this equilibrium point. c) Can you use Lyapunov indirect method to test the stability of the system? d) Use Lyapunov's theory to study the stability of the system. e) If the origin is L.A.S., then estimate the region of attraction.

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