Bifilar Pendulum w/ off-centred CM, need verification for derived eq.

Thread starter ChessGM
Start date Dec 31, 2024
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Center Centroid Pendulum

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The discussion centers on the derivation of equations related to a bifilar pendulum with an off-centered center of mass. A participant shares diagrams and results, prompting a request for the mathematical work behind those results. Another member offers to provide tips for posting mathematical content using LaTeX. The focus remains on verifying the derived equations and ensuring clarity in the mathematical presentation. The conversation emphasizes the importance of detailed mathematical explanations in physics discussions.

Dec 31, 2024

ChessGM

Homework Statement: For an essay I'm looking at the MOI about the central diameter of a composite object (2 flush concentric cylinders, the external cylinder is shorter lengthwise and can slide along the longer one) with a centre of mass that is not on the central diameter. This is done through the external cylinder, and placing it some distance from the centre, and timing its period in a bifilar pendulum.

I have an equation but I'm not sure if its correct, if anyone could take the time to come up with it and cross-reference it that would be appreciated.

Relevant Equations: The "standard" equation is 2 x pi x r x sqrt(IL/mg), but now it does not work because it assumes a centred centre of mass.

Here are some diagrams:

The mass of the rod is M, and the external cylinder is m. This is what I came up with:

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Dec 31, 2024

berkeman

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Can you show your math work that led to that result? I'll send you a message with tips for posting math here at PF using LaTeX.

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