# Solving Small Oscillations Homework: Find Equilibrium & Frequency

• pittiplatsch
In summary, the problem involves a particle of mass m and charge q moving along a vertical circle of radius R in a constant gravitational field of the earth. There is also another charge q fixed at the lowest point of the circle. The forces acting on the particle are the Coulomb forces exerted by the other charge, described by the equation F = q1q2/r^2. To find the equilibrium position and frequency of small oscillations, the potential energy must first be calculated. The two conditions required for this problem are that the particle is on a circular path and that there is another charge at the lowest point, but it is unclear how to express these conditions as equations. Assistance is needed to understand and solve this problem for an upcoming
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 teh circle.
Find the equilibrium position and the frequency of small oscillations of the particle.

## The Attempt at a Solution

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

Welcome to PF

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

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.

## What is the purpose of solving small oscillations homework?

The purpose of solving small oscillations homework is to understand the behavior of a system that undergoes small, repetitive motions around a stable equilibrium point. This type of homework helps students apply mathematical concepts such as equilibrium, frequency, and damping to real-world scenarios.

## How do you find the equilibrium point in a small oscillation problem?

To find the equilibrium point, you need to set the derivative of the system's position with respect to time equal to zero. This will give you the point at which the system is at rest and remains stable during small oscillations.

## What is the relationship between equilibrium and frequency in small oscillations?

The equilibrium point is directly related to the frequency of small oscillations. A higher frequency means the system oscillates more rapidly around the equilibrium point, while a lower frequency means the oscillations are slower. The equilibrium point is the point around which the system oscillates, so it is crucial in determining the frequency of the oscillations.

## How does damping affect small oscillations?

Damping is a force that opposes the motion of a system, causing it to lose energy and eventually come to rest. In small oscillations, damping affects the amplitude and frequency of the oscillations. A higher damping coefficient leads to smaller oscillations with a lower frequency, while a lower damping coefficient leads to larger oscillations with a higher frequency.

## What are some common techniques for solving small oscillations homework?

Some common techniques for solving small oscillations homework include using the equations of motion, setting up and solving differential equations, and applying mathematical concepts such as equilibrium, frequency, and damping. These techniques can help you analyze and understand the behavior of a system undergoing small oscillations.

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