# Analysis of 4 Equal Masses on a Circular Path

• jameson2
In summary, the problem involves finding the normal coordinates and frequencies of 4 equal masses connected by identical springs and constrained to move on a circle. It is not related to the motion of a mass-spring system in 1D and can be approached by using spherical-polar coordinates with the origin at the center of the circular loop. Each mass will have its own \theta coordinate.
jameson2

## Homework Statement

Given the system of 4 equal masses connected by identical springs, and constrained to move on a circle, find the normal coordinates and frequencies of the masses.

I'm not looking for the answer, just a push in the right direction as I'm having trouble starting. If someone could explain how this is related to the motion of springs and masses in a straight line system, it would be much appreciated.
Even a vague idea would be helpful, thanks.

jameson2 said:

## Homework Statement

Given the system of 4 equal masses connected by identical springs, and constrained to move on a circle, find the normal coordinates and frequencies of the masses.

I'm not looking for the answer, just a push in the right direction as I'm having trouble starting. If someone could explain how this is related to the motion of springs and masses in a straight line system, it would be much appreciated.
Even a vague idea would be helpful, thanks.

It's not really related to motions of the mass-spring system in 1D. You might want to consider spherical-polar coordinates with the origin at the center of the circular loop, that way the masses are given by a single coordinate: $\theta$.

I should note that you will actually have 4 $\theta$ coordinates, one for each mass. I hope I didn't introduce any confusion on that.

## 1. What is the purpose of analyzing 4 equal masses on a circular path?

The purpose of this analysis is to understand the forces and motion involved when four equal masses are moving in a circular path. This can help us understand the principles of circular motion and how forces interact with each other.

## 2. How do you calculate the centripetal force in this scenario?

The centripetal force in this scenario can be calculated using the formula Fc = mv^2 / r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.

## 3. What is the relationship between the mass and the centripetal force in this scenario?

The centripetal force is directly proportional to the mass of the objects. This means that as the mass increases, the centripetal force also increases, and vice versa.

## 4. How does the velocity of the objects affect the centripetal force?

The centripetal force is directly proportional to the square of the velocity. This means that as the velocity increases, the centripetal force also increases, and vice versa.

## 5. What are the potential risks or limitations of this analysis?

One potential risk of this analysis is assuming that the masses are perfectly equal and that there are no external forces acting on the system. In reality, there may be slight variations in mass and external forces such as friction that can affect the results. Additionally, this analysis may not account for other factors such as air resistance or changes in the circular path's radius.

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