We consider the problem of suspended particles in a rotating horizontal tube, filled with an almost inviscid fluid, which segregate into axial bands. Previous work has shown that inertial modes in the fluid are continuously excited by the particles. We observe that the system oscillates between two allowed modes. We derived a mean field model of the phenomena which describes the fluid-particle and particle-particle interactions in order to provide a deeper insight into the different states and evolution of the system. The model predicts relationships between the oscillation time period, the particle density and the fluid angular rotation frequency. These predictions were confirmed experimentally.