- #1

Felipe Lincoln

Gold Member

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- 11

## Homework Statement

A pendulum with a light rod of length ##l## with a bob of mass ##m## is released from rest at an angle ##\theta_0## to the downward vertical. Find its angular velocity as a function of θ, and the period of small oscillations about the position of stable equilibrium. Write down the solution for θ as a function of time, assuming that ##\theta_0## is small.

## Homework Equations

i) ## x=\theta l##

ii) ## F=-mg\sin\theta##

iii) ## V = mgl(1 - \cos\theta)##

iv) ## K+V=E##

## The Attempt at a Solution

## F## was obtained considering the equation i), the potential was obtained by doing ## F=-\dfrac{dU}{dx}## and them using the equation iv) we get the first answer, which is to find the angular velocity. The result is ##\omega=\pm\sqrt{\dfrac{2g}{l}(\cos\theta - \cos\theta_0)}##.

But what I can't understand is why isn't the angular velocity equal this: ## \omega=\sqrt{g/l}##

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