[mekrob]

Hey,

Given that most people on this board are pretty well educated, I thought I'd post this problem up here to see if I can get some direction with how to get the final question.

1. The problem statement, all variables and given/known data
A cart of mass M rides on four frictionlesly mounted wheels of radius a and mass m'. The top of the cart is sloped at an angle alpha horizontally and a mass m is suspended from the top of the slope of force constant k. m slides without friction up or down the slope.

a) Write the Lagrangian.
b) What is the frequency of oscillation of the mass m'.


2. Relevant equations
L= T-U
I (disk or wheel)= 1/2MR^2

3. The attempt at a solution
L= 1/2(m' + m +M)x'[sub]1[/sub][sup]2[/sup] + 2Iomega[sup]2[/sup] + 1/2(x[sub]1[/sub]' + x[sub]2[/sub]' + 2x[sub]1[/sub]'x[sub]2[/sub]'cos(alpha)) + mg(x[sub]2[/sub])sin(alpha) - 1/2k(x[sub]2[/sub])[sup]2[/sup]

x1 = position of M
x2 = position of m

I'm pretty sure that I got the Lagrangian right. This was a problem on a test (I'm studying for finals) and he didn't mark it wrong. I got most of the points for the problem, but I just couldn't find the frequency of oscillation of m'. Any help you guys can give?

If you're having a hard time understanding the math that I've written, I've posted it on another board here, where I'm not getting much help.

[Newsseeker]

I am in Physics right now but I have no clue how to help. Sorry.