In slide 9, why did you only linearize around the downward equilibrium point?
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Linearization was also done around the upward equilibrium point by using the small angle approximation of the sine function. This could be done in the upward case because the equilibrium point that we are linearizing around is zero; for the downward case, our equilibrium point was $\pi$ and so we weren't able to use that approximation.
--Julia Braman 16:09, 6 October 2008 (PDT)