Find x: Solving a Spring Stretch Problem

[elunicornhunte]

Homework Statement

A relaxed spring is sitting on a horizontal surface. A block attached at one of its ends is kicked, with a horizontal velocity, v1, given to it. The block will move and stretch. Find the distance, x, the spring will stretch. See figure. Find x in meters.

http://i.imgur.com/tYyl3t4.png

Homework Equations

F=-kx

The Attempt at a Solution

I used the equation ω=v/r to find the angular velocity = 1 rad/sec. I then thought that the angular velocity produces a centripetal force, which is the driving force for the spring to stretch. This centripetal force can be found using a=(ω^2)*r which = 1 m/s^2. I however, do not know how to use this force to find how far a spring would stretch when said force is applied. Any help is appreciated!

 

[nasu]

You forgot the figure?

 

[elunicornhunte]

Fixed it, there's a link in the OP.

 

[nasu]

That angular speed is for un-stretched spring, right?
The centripetal force is the elastic force of the spring. And this happens when the spring is stretched. So you have to write the angular frequency for stretched spring (r>lo).