Chapter 10, Problem 20RE

(a)

To determine

To show: When ${\omega }^2<\frac{g}{l}$ the point $\left(0,0\right)$ is stable critical point and $\left(0,0\right)$ is the only critical point in the domain $-\pi <\theta <\pi$.

(b)

To determine

To show: When ${\omega }^2>\frac{g}{l}$ the point $\left(0,0\right)$ is unstable critical point and there are two additional stable critical points $\left(\pm \widehat{\theta },0\right)$ in the domain $-\pi <\theta <\pi$.