Question

why does the compound pendulum have the identity of possessing two values of h corresponding to the same period of oscillator r ?

Answer 1

The compound pendulum

Let G be the centre of gravity of a compound pendulum of mass m that oscillates about a point O with OG = h If the pendulum is moved so that the line OG is displaced through an angle θ (Figure 1), the restoring couple is: ... where k is the radius of gyration about a parallel axis through G.