Answer Happy

4. Take the damped nonlinear pendulum equation 0 +10° + sin 0 = 0 for some p > 0 (1.e., there is some friction). See the lecture notes and/or textbook (Chapter 8) for the meaning of each variable. (a) Suppose d = 1 and 2 = 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 x > 0 and any (d) Classify each equilibrium found in the previous subquestion under the assumption that the damping is small, in particular, ? < (c) Explain what your findings mean, and if it agrees with what you expect in reality,