Adopting the Narimanov-Moiseev–type asymptotic modal method, the free-surface boundary problem on a freely levitating drop is revisited to construct a periodic solution describing weakly-nonlinear axisymmetric drop motions with a frequency close to the lowest linear natural frequency whose value is predicted by Lord Rayleigh. The soft-spring–type amplitude-frequency dependence following from this periodic solution is validated by existing experimental and numerical results.