# Homework Help: SHM of cube from an edge

1. Feb 22, 2015

### 1bigman

1. The problem statement, all variables and given/known data
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 $T = 2\pi \sqrt{\frac{7\sqrt{2}a}{9g}}$
2. Relevant equations

3. 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

Last edited: Feb 22, 2015
2. Feb 22, 2015

### 1bigman

Ah, turns out the moment of inertia was incorrect.....