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Condition for Simple Harmonic Motion

  1. Apr 14, 2014 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    a small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least R/r ratio such that the object performs simple harmonic motion.

    3. The attempt at a solution

    For the object to perform SHM it must be in a stable equilibrium position. So, its potential energy must be minimum at the mean position. But how do I express it mathematically?
     
  2. jcsd
  3. Apr 14, 2014 #2
  4. Apr 14, 2014 #3

    utkarshakash

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    Gold Member

    Hmm that's a really long post and I think I should better leave this question as it would be too time consuming. btw Thanks for help!
     
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