  We studied the dynamical properties of Rabi oscillations driven by an
alternating Rashba field applied to a two-dimensional (2D) harmonic confinement
system. We solve the time-dependent (TD) Schr\"{o}dinger equation numerically
and rewrite the resulting TD wavefunction onto the Bloch sphere (BS) using two
BS parameters of the zenith ($\theta_B$) and azimuthal ($\phi_B$) angles,
extracting the phase information $\phi_B$ as well as the mixing ratio
$\theta_B$ between the two BS-pole states.
  We employed a two-state rotating wave (TSRW) approach and studied the
fundamental features of $\theta_B$ and $\phi_B$ over time. The TSRW approach
reveals a triangular wave formation in $\theta_B$. Moreover, at each apex of
the triangular wave, the TD wavefunction passes through the BS pole, and the
state is completely replaced by the opposite spin state. The TSRW approach also
elucidates a linear change in $\phi_B$. The slope of $\phi_B$ vs. time is equal
to the difference between the dynamical terms, leading to a confinement
potential in the harmonic system. The TSRW approach further demonstrates a jump
in the phase difference by $\pi$ when the wavefunction passes through the BS
pole.
  The alternating Rashba field causes multiple successive Rabi transitions in
the 2D harmonic system. We then introduce the effective BS (EBS) and transform
these complicated transitions into an equivalent "single" Rabi one.
Consequently, the EBS parameters $\theta_B^{\mathrm{eff}}$ and
$\phi_B^{\mathrm{eff}}$ exhibit mixing and phase difference between two spin
states $\alpha$ and $\beta$, leading to a deep understanding of the TD features
of multi-Rabi oscillations. Furthermore, the combination of the BS
representation with the TSRW approach successfully reveals the dynamical
properties of the Rabi oscillation, even beyond the TSRW approximation.
