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1bigman
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Homework Statement
We have a cubical hollow box, edge length ##a## suspended horizontally from a frictionless hinge along one of its edges. The box is displaced slightly and undergoes SHM. Show that the period of the oscillation is given by ## T = 2\pi \sqrt{\frac{7\sqrt{2}a}{9g}} ##
Homework Equations
The Attempt at a Solution
##E_{tot} = \frac{1}{2}I\omega^2 + mg\left(\frac{\sqrt{2}}{2a}\cos\theta\right) ##Then apply taylor expansion and differentiate to get: ## \ddot\theta = \frac{mga}{\sqrt{2}I} \theta ## and using ##I = \frac{2}{3}ma^2## gives ##T = 2\pi \sqrt{\frac{2\sqrt{2}a}{3g}}##
Help is much appreciated
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