A particle is tied to an extensible string, which obeys Hooke's Law and performs circular motion with speed v and radius 2r on a horizontal smooth table. The natural length of the string is r. The speed of the particle is slowly increased such that the string's length becomes 3r. Find the new speed of the particle.

edit: upon reading the sticky.. here's my attempt

Applying

F=-kx

F=mv^2/r

when speed=v, radius = 2r

F=mv^2/2r

F=-k(2r-r)

when radius =3r,

F=mv^2/3r

F=-k(3-r)

Here's where I'm stuck.