= 4. Take the damped nonlinear pendulum equation 0" + po' + { sin 0 = 0 for some pi > 0 (i.e., there is some friction).

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4 Take The Damped Nonlinear Pendulum Equation 0 Po Sin 0 0 For Some Pi 0 I E There Is Some Friction 1 (121.55 KiB) Viewed 21 times

= 4. Take the damped nonlinear pendulum equation 0" + po' + { sin 0 = 0 for some pi > 0 (i.e., there is some friction). See the lecture notes and/or textbook (Chapter 8) for the meaning of each variable. = (a) Suppose u = 1 and į = 1. Find all the equilibria. (b) Classify each equilibrum found in the previous subquestion. In other words, is each equi- librium a source, sink, saddle, center point, spiral source, spiral sink, or something else? Justify your answer (just stating the final result does not earn points). 1 (c) Find all the equilibria for any p > 0 and any I. (d) Classify each equilibrium found in the previous subquestion under the assumption that the damping is small, in particular, je? < 19. (e) Explain what your findings mean, and if it agrees with what you expect in reality.