You probably have noticed that, as you increase ω, there will be a value, ωcrit, for which r(ω) goes to infinity. find ωcrit. answer in terms of k and m.

For the mass m, attached to a spring, to move in a circle centripetal force and restoring force of the spring must be equal. Centripetal force is given with this formula:

Restoring force only occurs if the spring is stretched. If L is the length of unstretched spring we have the following formula for restoring force:

r is the length of a circle that mass m is traveling along. 
As said above, these two forces have to be equal:

We solve for r:

r(w) will go to infinity when denominator is equal to zero:

Please keep in mind that Hooke's law has it's limitations, and before we reach our critial value of angular velocity spring will be strecthed to a point where Hooke's law does not aply anymore.

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