  The geometrical representation of two-flavor neutrino oscillation represents
the neutrino's flavor eigenstate as a magnetic moment-like vector that evolves
around a magnetic field-like vector that depicts the Hamiltonian of the system.
In the present work, we demonstrate the geometrical interpretation of neutrino
in a vacuum in the presence of decay, which transforms this circular trajectory
of neutrino into a helical track that effectively makes the neutrino system
mimic a classical damped driven oscillator. We show that in the absence of the
phase factor $\xi$ in the decay Hamiltonian, the neutrino exactly behaves like
the system of nuclear magnetic resonance(NMR); however, the inclusion of the
phase part introduces a $CP$ violation, which makes the system deviate from
NMR. Finally, we make a qualitative discussion on under-damped,
critically-damped, and over-damped scenarios geometrically by three different
diagrams. In the end, we make a comparative study of geometrical picturization
in vacuum, matter, and decay, which extrapolates the understanding of the
geometrical representation of neutrino oscillation in a more straightforward
way.
