We apply the hyperspherical (HS) method to study a Bose-Einstein condensate in quasi-two-dimensional free space stabilized and confined under the influence of an oscillating magnetic field. The HS method indeed reproduces stabilized breathing mode solutions qualitatively similar to those previously obtained by the Gross-Pitaevskii (GP) equation. Also, the frequencies of our breathing mode solutions are shown to have functional dependence on the physical parameters in a manner similar to the GP results. However, beats in the breathing mode solutions are revealed in the HS approximation, while they are seemingly absent in the GP descriptions. A supplementary analysis of the stationary state solutions shows that the hyperspherical single-particle density exhibits certain characteristic scaling dependence on energy akin to the Townes soliton [Chiao et al., Phys. Rev. Lett. 13, 479 (1964)], but also some difference in detail. The Kapitza averaging leads to an effective time-independent potential and shows how continuously distributed hyperspherical ``bound'' states turn into discrete ``bound'' states on accounting of the modulating field. The HS method is made subject to the Floquet analysis in order to interpret the beats in the breathing mode as coherent excitation among discrete Floquet states.