**Take the damped nonlinear pendulum equation $ \ \ θ′′ + μθ′ + (g/L) \ sin θ = 0 \ $ for some μ > 0 (that is, there is some friction)

Question

Take the damped nonlinear pendulum equation $ \ \ θ′′ + μθ′ + (g/L) \ sin θ = 0 \ $ for some μ > 0 (that is, there is some friction). a) Suppose μ = 1 and $ \frac{g}{L} = 1 $ for simplicity, find and classify the critical points. b) Do the same for any μ > 0 and any g and L, but such that the damping is small, in particular, $ μ^{2} < 4(\frac{g}{L}) $. $$ $$ (a) If $ \mu=1 \ \ and \ \ \frac{g}{L}=1 $ , then the equation becomes $ \theta''+\theta'+\frac{g}{L} \sin \theta =0 $. Let $ w=\theta' $ , then the equation becomes a 2 dimensional system as follows \begin{align} w'=-w+\frac{g}{L}\sin \theta \\ \theta'=w \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \end{align}. Then the critical points are obtained from \begin{align} w'=0 \ \ implies\ \ w-g/L \sin \theta=0 , \\ \theta'=0 \ \ implies \ \ w=0, \end{align}. Hence the critical points are $ (0,0) , (0 , \pi ) , ..... $ . Am I right ? and what the part (b) ? please help me