What are the Normal Mode Frequencies for a Hanging Rod's Vertical Oscillation?

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Homework Help Overview

The discussion revolves around determining the normal mode frequencies of a uniform rod that hangs vertically from an inelastic string. The problem involves analyzing the oscillation of the rod in the vertical plane, considering its length and the attachment point of the string.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to set up the problem using angles related to the string and rod but expresses uncertainty about how to treat the mass of the rod. Some participants question the treatment of mass and suggest focusing on the center of mass and kinetic energy terms.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Guidance has been offered regarding the calculation of the center of mass and kinetic energy, but there is no explicit consensus on the approach to take.

Contextual Notes

There is a mention of the string being massless, which may influence the assumptions made in the problem setup. The original poster has not provided a complete setup or solution, indicating a need for further exploration of the problem.

benij_chaos
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I Have a question that is bugging me because I can't get the answer out here's the question:

A uniform rod of length a hangs vertically on the end of an inelastic string of length a, the string being attached to the upper end of the rod. What are the frequencies of the normal modes of oscillation in the vertical plane.

Any help would be appreciated thanks
 
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benij, it is required that you show your thoughts/efforts when asking for help with coursework/textbook problems.
 
I set the problem up with two angles, one that joins the string to the vertical and one that joins the string to the rod. My problem comes in not knowing how treat the mass in the question. I have tried dividing it up into two parts and that does not seem to work. I am effectively stuck before I am started.
 
Can you find the velocity of the center of mass of the rod, in terms of the lengths and angles (and their derivatives)? From v(COM) and the angular velocity about its top end, you can then write down the total kinetic energy term, T.

PS: I don't know what 2 masses you are talking about. The string is massless.
 
Last edited:

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