A physical pendulum is positioned so that its centre of gravity is above the suspension point. When the pendulum is realsed it passes the point of stable equilibrium with an angular velocity `omega`. The period of small oscollations of the pendulum is

Explanation

Let `l=` distance the C.G. `(C)` of the pendulum and its point of suspension `O` . Oringinally the pendulum is in inverted position and its C.G. is above `O`. When it falls to the notmal (stable) position of equilibrium its C.B. has fallen by a distance `2l`. In the equilibrium position the total energy is equal to `K.E.=(1)/(2) I omega^(2)` and we have from energy conservation `:`
`(1)/(2)I omega^(2)=mg2l `or `I=(4mgl)/(omega^(2))`
Angular frequency of oscillation for a physical pendulum is given by `omega_(0)^(2)=mgl//I`
Thus `T=2pisqrt((I)/(mgl))=2pi sqrt((4mgl//omega^(2))/(mgl))=(4pi)/(3)`