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Man I hate to make two post in one day but I am really stuck!

A particle slides on the inside surface if a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half angle of the tip is α. Let r be the distance from the particle to the axis, and let θ be the angle around the cone.

1. Find the equations of motion.

2. If the particle moves in a circle of radius r_0, what is the frequenct of this motion ω?

3. If the particle is perturbed slightly from the circular motion, what is the frequency of oscillations about the radius r_0?

Lagrangian and Lagranges Equations

If need be, I will draw a picture and upload it so the relations used are more obvious.

First thing is first, is my Lagrangian correct? (I made an image in MathType, its easier for me.)

[PLAIN]http://img197.imageshack.us/img197/9997/lag1.gif [Broken]

I do not think this is correct because I am not getting oscillatory motion for theta when I solve!

EDIT: Oh! I forgot to mention! 'l' is the distance on the side of the cone from the point to where the particle is. I do not know how to include this in the lagrangian!

## Homework Statement

A particle slides on the inside surface if a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half angle of the tip is α. Let r be the distance from the particle to the axis, and let θ be the angle around the cone.

1. Find the equations of motion.

2. If the particle moves in a circle of radius r_0, what is the frequenct of this motion ω?

3. If the particle is perturbed slightly from the circular motion, what is the frequency of oscillations about the radius r_0?

## Homework Equations

Lagrangian and Lagranges Equations

## The Attempt at a Solution

If need be, I will draw a picture and upload it so the relations used are more obvious.

First thing is first, is my Lagrangian correct? (I made an image in MathType, its easier for me.)

[PLAIN]http://img197.imageshack.us/img197/9997/lag1.gif [Broken]

I do not think this is correct because I am not getting oscillatory motion for theta when I solve!

EDIT: Oh! I forgot to mention! 'l' is the distance on the side of the cone from the point to where the particle is. I do not know how to include this in the lagrangian!

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