Sliding sleeve on a rotating bar with two springs

AI Thread Summary
The discussion focuses on determining the period of small oscillations for a sleeve fixed between two springs on a rotating bar. The relevant equation for the period is T=2π/(k/m-ω²)^(1/2). Participants express difficulty in solving the problem without using pseudo forces and inquire about alternative methods, particularly in polar coordinates. There is a consensus that polar coordinates may be necessary for a proper solution. The conversation highlights the challenges of applying different approaches to 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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