The equation of motion for a particle moving on a rotating circular frame (Figure SP12.45) is

\[\ddot{\theta}+\frac{g}{R}\left(\sin \theta-\frac{\omega^{2}}{g} \cos \theta\right)=0\]

(a) Determine the equilibrium points.

(b) Classify the equilibrium points and determine their stability for

(i) \(\frac{\omega^{2}}{g}=0.5\)

(ii) \(\frac{\omega^{2}}{g}=1\)

(iii) \(\frac{\omega^{2}}{g}=1.5\)

Transcribed Image Text:

(b) FIGURE SP12.45 00