Particle in gravitational field

[Math Jeans]

Homework Statement

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

$$\omega=\sqrt{\frac{2g}{a+z_0}}$$

Homework Equations

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?

 

[tiny-tim]

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

$$\omega=\sqrt{\frac{2g}{a+z_0}}$$

Hi Math Jeans!

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.