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.

The radiation of the fire causes the saucepan to heat up. the conduction of the saucepan then to distribute the heat over the saucepan and to give heat to the water. the convection of the water distributing the heat within the water, till all the water is boiling