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mekrob
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Homework Statement
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'.
Homework Equations
L= T-U
[tex]I(for disk/wheel)=1/2MR^2[/tex]
The Attempt at a Solution
[tex]L= 1/2 (4m'+M+m)\dot{x}_{1}^2 + 2I (\omega)^2 + 1/2m(\dot{x_{1}}+\dot{x_{2}} + 2\dot{x_{1}} \dot{x_{2}}cos(\alpha)) + mgx_{2}sin(\alpha) - 1/2kx_{2}^2[/tex]
x1 = position of M
x2 = position of m
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