 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2013/9/b/solution

2 M R^{2} \ddot{θ} + M g R sin θ = 0

. Linearizing about

θ = 0

gives

ω_{fixed} = \frac{g}{2 R}, f_{fixed} = \frac{1}{2 π} \frac{g}{2 R}, T_{fixed} = 2 π \frac{2 R}{g} .

Both angular frequency and ordinary frequency are given to distinguish the two conventions. The stable position places the extra mass below the pivot.

 New to topics? Read the docs here!