  Understanding the collective dynamics in a many-body system has been a
central task in condensed matter physics. To achieve this task, we develop a
Hartree-Fock theory to study the collective oscillations of spinor Fermi
system, motivated by recent experiment on spin-9/2 fermions. We observe an
oscillation period shoulder for small rotation angles. Different from previous
studies, where the shoulder is found connected to the resonance from periodic
to running phase, here the system is always in a running phase in the two-body
phase space. This shoulder survives even in the many-body oscillations, which
could be tested in the experiments. We also show how these collective
oscillations evolve from two- to many-body. Our theory provides an alternative
way to understand the collective dynamics in large-spin Fermi systems.
