Period of vibration for rod AB with sliding collars

[chart2006]

Homework Statement

The slender rod AB of weight $$W_{AB}$$ is attached to two identical collars, each of weight $$W$$. The system lies in a horizontal plane and is in equilibrium in the position shown when the collar A is given a small displacement and released. Calculate and plot the period of vibration for values of the angle β from 10 to 80 degrees for weight ratios $$\frac{W}{W_{AB}}$$ of 0, 2, and 4.

http://image.cramster.com/answer-board/image/20095101932446337758076418525009540.jpg

I'm looking for help as to how to set the problem up that's all! Any help is appreciated!

Homework Equations

The Attempt at a Solution

 

[diazona]

What does the k in the diagram represent?

 

[physicsnoob93]

spring constant, i would guess.

 

[chart2006]

Yes it's the spring constant