In Fig 15.19a, a meter stick swings about a pivot point at one end, at distance h from the stick's center of mass.
What is the period of oscillation T?

Solution :The stick is not a simple pendulum because its mass is not concentrated in a bob at the END opposie the pivot point- so the stick is a physical pendulum.
Calculations: The period for a physical pendulum is given by Eq 15.45, for which we need the rotational inertia I of the stick about the pivot point. We can treat the stick as a uniform rod of length L and mass m. Then `I= 1//3mL^(2)`, and the distance H in Eq. 15.45 is 1/2L. Substituting these QUANTITIES into Eq. 15.45, we find
`T= 2PI sqrt((I)/(mgh)) = 2pi sqrt(((1)/(3)mL^(2))/(mg((1)/(2)L)))`
`=2pi sqrt((2L)/(3g))`
`=2pi sqrt(((2)(1.00m))/((3)(9.8m//s^(2))))= 1.64s`
Note: the result is independent of the pendulum.s mass m.