. Suppose we take / = 9.8 m (so g/l = 1), m = 1, and b large, say b = 4. For the damped pendulum system above and with this choice of parameter values, do the following. (a) Find the cigenvalues and cigenvectors of the linearized system at the equilib- rium point (0, 0). (b) Find the eigenvalues and eigenvectors of the linearized system at the equilib- rium point (7, 0). (c) Sketch the phase portrait near the equilibrium points. (d) Sketch the entire phase portrait. [Hint: Begin by sketching the level sets of H as in the text.]

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