Sliding sleeve on a rotating bar with two springs

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Homework Help Overview

The problem involves a sleeve on a rotating bar that is influenced by two identical springs. The context is centered around dynamics and oscillatory motion, specifically examining the conditions for small oscillations and the effects of angular velocity on the system's behavior.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive the period of small oscillations using a pseudo force approach but is uncertain about applying a more conventional method. They question whether it is possible to analyze the system without pseudo forces. Other participants inquire about expressing acceleration in polar coordinates, indicating a potential avenue for exploration.

Discussion Status

The discussion is ongoing, with participants exploring different methods of analysis. There is no explicit consensus on the best approach, but the conversation is focused on understanding the dynamics involved and the applicability of polar coordinates.

Contextual Notes

One participant mentions that polar coordinates are not part of their curriculum, which may limit their ability to engage with that aspect of the problem.

andyrk
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Homework Statement


P45) In the arrangement shown in figure, the sleeve M of mass m is fixed between two identical springs whose combined stiffness is equal to k. The sleeve can slide without friction over a horizontal bar AB. The arrangement rotates with a constant angular velocity w about a vertical axis passing through the middle of the bar. Find the period of small oscillations of the sleeve. At what values of w will there be no oscillations of the sleeve?



2. Homework Equations
T=2âˆ/(k/m-ω2)1/2


The Attempt at a Solution


I got this answer by following the pseudo force approach but got stuck when I tried to do it with the normal method without pseudo force. Can we do it without using pseudo forces? And if yes then how?
 

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Is anyone there to reply?
 
Are you familiar with how to express acceleration in polar coordinates?
 
No. Its not in the curriculum I am doing.
 

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