If x0 is a sink for the system x' = F(x), then the basin of attraction for x0 is the set of points y = [y1, y2]T which have the property that the solution curve through y approaches x0 as t → +∞. Consider the damped pendulum with damping constant a − 0.5. Find the basin of attraction for [0,0]T. You should indicate this region on a printed output of pplane6. Hint: It will be extremely helpful to plot the stable and unstable orbits from a couple of saddle points.
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