A particle of mass \(m\), and angular momentum \(\ell\) is moving in a circular orbit of radius \(r_0\) under the influence of an attractive force \(\vec{F}(r) = -\frac{k}{r^2}\hat{r}\). Keeping its angular momentum unchanged, the particle is displaced radially by a small distance \(\delta r \ll r_0\), due to which its radial distance varies periodically. The corresponding time period is: