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Homework Help: Particle in gravitational field

  1. Nov 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider a particle of mass m constrained to move on the surface of a paraboloid whose equation (in cylindrical coordinates) is [tex]r^2=4az[/tex]. If the particle is subject to a gravitational force, show that the frequency of small oscillations about a circular orbit with radius [tex]\rho=\sqrt{4az_0}[/tex] is

    [tex]\omega=\sqrt{\frac{2g}{a+z_0}}[/tex]

    2. Relevant equations



    3. The attempt at a solution

    The problem that I'm having is that I don't understand the wording of the question?

    How do I draw out this scenario?
     
  2. jcsd
  3. Nov 28, 2008 #2

    tiny-tim

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    Homework Helper

    Hi Math Jeans! :smile:

    It means that the ball is freely rotating (I don't know why they call it oscillating) around a horizontal circle at height z0 (so the radius is √4az0).

    I think the word "small" means that you can pretend that eg sinx = x.

    Use Newton's second law to find the angular velocity, and therefore the frequency of the rotation. :smile:
     
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