Rod Aluminum

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How to find the physical period of the pendulum?

A pendulum is constructed from a thin, rigid, and uniform rod with a small sphere attached to the end opposite the pivot. This arrangement is a good approximation to a simple pendulum (period = 6.25 s), because the mass of the sphere (lead) is much greater than the mass of the rod (aluminum). When the sphere is removed, the pendulum is no longer a simple pendulum, but is then a physical pendulum. What is the period of the physical pendulum?

given T = 2 pi square root of (L / g) = 6.25 sec

and for a physical pendulum T' = 2 pi square root of ( I / mg Lcm)
where, I = moment of inertia of rod = m L^2 / 3, Lcm = L / 2

so that T' = 2 pi square root of ( 2 L / 3 g )

= square root of (2/3) T = square root of (2/3) x 6.25
= 5.1 sec (nearly)

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