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Sliding sleeve on a rotating bar with two springs

  1. Dec 22, 2013 #1
    1. The problem statement, all variables and given/known data
    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. Relevant equations
    T=2âˆ/(k/m-ω2)1/2



    3. 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?
     

    Attached Files:

  2. jcsd
  3. Dec 22, 2013 #2
    Is anyone there to reply?
     
  4. Dec 22, 2013 #3

    TSny

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    Are you familiar with how to express acceleration in polar coordinates?
     
  5. Dec 22, 2013 #4
    No. Its not in the curriculum I am doing.
     
  6. Dec 22, 2013 #5

    TSny

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