Calculating the Period of SHM for a Suspended Cubical Box

[1bigman]

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

 

[1bigman]

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