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**SOS .. Problem with lagrange derivation!**

## Homework Statement

Im having a hard time with the problem illustrated in the following figure:

[URL=http://img199.imageshack.us/i/20091224344.jpg/][PLAIN]http://img199.imageshack.us/img199/812/20091224344.th.jpg[/URL][/PLAIN]

it said that solve the equations of motion for a coupled oscillators system consists of a metallic smooth ring of mass M and radius R oscillates in its own plane with one point fixed, along with it a particle of mass M sildes without friction on it. This particle is attached to the point of support of the ring by a massless spring of stiffness constant k and unstreched length 2R, taking in consideration only small oscillations about the equilibrium configuration

In this problem the given parameters are as follows:

R (radius) = 4.0 cm ,

M (mass) = 13.0 g,

k (spring constant) = 8.0 N/m

## Homework Equations

I have to get somehow to the following equations

[URL=http://img40.imageshack.us/i/20091226346.jpg/][PLAIN]http://img40.imageshack.us/img40/2695/20091226346.th.jpg[/URL][/PLAIN]

## The Attempt at a Solution

i was thinking that for the sliding mass, x=2Rcos(theta+phi) and y=2Rsin(theta+phi)

and for the ring its x=2Rsin(theta) and y = 2Rcos(theta).. and then the potential energy of the system would be = -2Rmgcos(theta)-2Rcos(theta+phi)

and the kinetic energy is = 0.5*m*(x-dot^2(for the sliding mass) + x-dot^2(for the ring)

I know what I am doing is wrong coz no matter how i look at the questions I still can't find out how to reach the equations they reached..

I appreciate any help .. thanks in advance ..