Oscillations of a Balanced Object

[breid040]

Homework Statement

Two identical thin rods, each of mass m and length L, are joined at right angles to form an L-shaped object. This object is balanced on top of a sharp edge. If the object is displaced slightly, it oscillates. Find ω, the angular frequency of oscillation of the object.

Relevant Equations

ω=Sqrt(mgd/I)

I calculated that the distance from the pivot to the center of mass was sqrt(2) L/4, and that the moment of inertia was 1/6mL^2+2m(L/2)^2. I simplified the moment of inertia to 2/3mL^2, and the 2mgd to sqrt(2)mgL. Cancelling out the m's and the L's, I end up with sqrt(3sqrt(2)g/2L). It says that this is incorrect, however, and I'm not sure why. Any help is appreciated.

 

[breid040]

I figured it out myself, haha. I was accidentally multiplying the mgd by 4 instead of 2. I got the right answer.