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**1. 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.

**2. 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

**3. 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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