Chapter 10.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation ${\theta }^{″}+\sin \theta =\frac{1}{2}$ are $\left(\frac{\pi }{6},0\right)\text{ and }\left(\frac{5\pi }{6},0\right)$.

(b)

To determine

The nature of the critical point $\left(\frac{5\pi }{6},0\right)$ by linearization.

(c)

To determine

The nature of the critical point $\left(\frac{\pi }{6},0\right)$ by phase plane method.