Exercise 101

Take the damped nonlinear pendulum equation $\theta '' + \mu \theta' + (\nicefrac{g}{L}) \sin \theta = 0$ for some $\mu > 0$ (that is, there is friction). Suppose the friction is large, in particular $\mu^2 > 4 (\nicefrac{g}{L})$.

1. Find and classify the critical points.
2. Explain what your findings mean, and if it agrees with what you expect in reality.