Mechanics Problem: Time Period of Simple Pendulum with Uniform Rod and Mass m

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The discussion centers on calculating the time period of a simple pendulum when a uniform rod replaces the string, introducing a mass M and altering the center of mass. The problem highlights that the system now behaves as a physical pendulum due to the rod's mass. Participants note that the moment of inertia is crucial for determining the new time period, which requires deriving the appropriate relation. The change in the center of mass and the moment of inertia are emphasized as key factors in solving the problem. Understanding these concepts is essential for accurately calculating the time period of small oscillations in this modified pendulum setup.
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Homework Statement



In a simple pendulum the string supporting the bob is replaced by a uniform rod of length L and mass M.Find the nw time period for small oscillations.Mass of the bob m.

Any help how to do it correctly?

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The Attempt at a Solution



Any help how to do it correctly?
 
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i guess the mass of string was neglected
and now since the rod has mass M, the CG of the system has changed
 
Basically, this is a physical pendulum now. Sure, the centre of mass has changed. So has the moment of inertia. If I remember right, the moment of inertia of a physical pendulum determines its period, but you'll have to derive the exact relation.
 

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