$A$ spring-mass system (mass $m$,spring constant $k$,and natural length $\ell_{0}$) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the center of the disc. If the disc,together with the spring-mass system,rotates about its axis with an angular velocity $\omega$ (where $k >> m \omega^{2}$),the relative change in the length of the spring is best given by which option?

• A
  $\frac{2 m \omega^{2}}{k}$
• B
  $\frac{m \omega^{2}}{3 k}$
• C
  $\sqrt{\frac{2}{3}}\left(\frac{m \omega^{2}}{k}\right)$
• D
  $\frac{m \omega^{2}}{k}$