Sliding sleeve on a rotating bar with two springs

[andyrk]

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?

 

[andyrk]

Is anyone there to reply?

 

[TSny]

Are you familiar with how to express acceleration in polar coordinates?

 

[andyrk]

No. Its not in the curriculum I am doing.

 

[TSny]

I'm afraid I don't see a nice way to do it other than using polar coordinates .