General

Physics problem help

So, this last problem on my final completely destroyed me, and it's been bugging me ever since I got back home. Can someone solve this and show me the work so my soul can be at peace?

My physics professor called it a Gyroscope of Doom, by the way.

Suppose there is an L-shaped rod (think half of a square's perimeter), with a side length L and total mass M. The rod is attached to the z-axis at the origin but is tilted an angle T below the xy plane, so it makes some sort of a tilted letter 'V' when viewed horizontally. At the end of the rod is a disc of radius R and mass M, which is spinning at an angular velocity w. Gravity is acting on the system's center of mass (not given). In addition, a spring of rest length 0 and spring constant k is attached to the z-axis below the pivot of the L-shaped rod (makes an isosceles triangle), and its other end is attached to the L-shaped rod at its corner. The torque exerted by gravity and the spring causes a change in angular momentum that causes the gyroscope system to rotate around the z-axis. The entire system is viewed from a reference frame C', which is travelling in the positive z direction at a velocity v. What is the period of precession, Q', of the gyroscope system as viewed from reference frame C'?

The problem should look like this: http://i286.photobucket.com/albums/ll92/cb000/GyroscopeofDoom.png

Come to think of it, this problem might have seemed impossible at the time because I'd gone through 7 other problems and had like 30 minutes left. I'll also work on it again and see how I do without the pressure.

Edit: some of the symbols I pulled off MS word aren't showing properly. Let me switch them.
Edit 2: Switched the small omega with w and the big omega with Q. Also, theta has been replaced by...uhh, T.