The original length of the spring with stiffness coefficient K is lo. One end of the spring is tied to the vertical axis, and the other end is tied to a small ball with mass m to make uniform circular motion on a smooth horizontal plane When the spring elongation is l, what is the angular velocity of the metal ball rotating around the vertical axis?

The original length of the spring with stiffness coefficient K is lo. One end of the spring is tied to the vertical axis, and the other end is tied to a small ball with mass m to make uniform circular motion on a smooth horizontal plane When the spring elongation is l, what is the angular velocity of the metal ball rotating around the vertical axis?

The spring force provides centripetal force
It should be noted that if the elongation is l, then the radius of motion of the ball is lo + L
kL=mω²(Lo+L)
ω=√[kL/m(Lo+L)]