Finding Spring Constant for Rotational Motion Problem

[Adel A]

Homework Statement

(Sorry for my bad English)
A slippery (frictionless), light horizontal bar rotates about a vertical axis with a constant angular velocity ω. A cylinder with mass m, is initially attatched to a thread with length a and to a spring, which from the beginning has its "natural" length.
Suddenly the thread breaks. Now the maximum distance between the cylinder and the axis is b.
Determine the spring constant k for the spring.

I have uploaded a picture of the problem.

Thanks!

Homework Equations

The Attempt at a Solution

I know that I should use integration but I don't know how or where to start.

 

[Chestermiller]

You must know some equations that apply to circular motion, and you must know an equation (or equations) that describe the behavior of springs. Please write them under relevant equations.

Start (as usual) by drawing a free body diagram of the mass. What are the forces acting on the mass (after the string is cut)?

Chet