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armis
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Homework Statement
Determine the period of oscillations of a simple pendulum ( a particle of mass m suspended by a string of length l in a gravitational field) as a function of the amplitude of oscillations.
Homework Equations
[tex] T(E) = \sqrt(2m) \int^{x_2(E)}_{x_1(E)}\frac{dx}{\sqrt(E-U(x)} [/tex]
where T is the period of oscillations
The Attempt at a Solution
I only need the expression of E(x) and the problem is pretty much solved but I can't figure out why (which is rather embarassing ) the energy of the pendulum
[tex] E = \frac{1}{2}ml^2{\phi}^2 - mgl\cos{\phi} = -mgl\cos{\phi_o} [/tex]
where [tex] \phi [/tex] is the angle between the string and the vertical and [tex] \phi_0 [/tex] the maximum value of [tex] \phi [/tex]
Any hints?
thanks
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