- #1
jimz
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Homework Statement
Find the period of oscillation of a bead on a cycloid string. If it matters, the original equations of the cycloid were
[tex]x=a(\theta-sin\theta)[/tex] and [tex]y=a(1+cos\theta)[/tex]
Homework Equations
This is a small part of a larger problem... I found the equation of motion of a bead on a cycloid to be:
[tex]\ddot{u}+\frac{g}{4a}u=0[/tex]
where [tex]u=cos(\frac{\theta}{2})[/tex]
using Lagrange which is correct.
I think I recall period being:
[tex]T=\frac{2\pi}{\omega}[/tex]
also [tex]\omega=\frac{\dot{v}}{r}[/tex]
The Attempt at a Solution
Not really sure. All I can do is:
[tex]\ddot{u}=-\frac{1}{4}cos(\frac{\theta}{2})[/tex]
and then I don't know what to do.
Any help is greatly appreciated. I even know the answer but can't see how to get there, so obviously this one must be embarrassingly easy.
[tex]T=2\pi\sqrt{\frac{4a}{g}}[/tex]
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