Solving Small Oscillations Homework: Find Equilibrium & Frequency

[pittiplatsch]

Homework Statement

A particle of mass m and charge q can move along a vertical circle of radius R in the constant gravitational field of the earth. Another charge q is fixed to the lowest point of the circle.
Find the equilibrium position and the frequency of small oscillations of the particle.

Homework Equations

The Attempt at a Solution

I'm really lost and have no idea how to solve this problem. Any help would be great...

 

[Redbelly98]

Welcome to PF

You can start by listing the forces that act on the particle. What expressions/equations describe those forces?

 

[pittiplatsch]

Hi RedBelly,

Thanks for your reply. I would say the forces acting on the particle are the coulomb forces exerted on it by the other charge. the corresponding equation is

F = q1q2/r^2, but I'm not sure if this is the only force acting on it, because there must be another force that keeps it to move on the circular path.

I think I first have to fnd the potential energy so that I can find both the equilibrium position and the frequency of small oscillations, but I still don't know how to do that, especially as I have no idea how express the two conditions

1) that the particle be on a circular path and
2) that there be another charge at the lowest point

by an equation.

Please help me! I really need to understand this because I will soon have an exam where this kind of questions will be asked.