The multifrequency resonance has been widely explored in some of the single-particle models, in which the modulating Rabi model has been most widely investigated. It has been found that with the diagonal periodic modulation, a steady dynamics can be realized in some well-defined discrete frequencies. These frequencies are independent of the off-diagonal couplings. In this work, we generalize this physics to the many-body seesaw realized using the tilted Bose-Hubbard model. We find that the wave function will recover to its initial condition when the modulation frequency is commensurate with the initial energy level spacing between the ground and the first excited levels. The period is determined by the driving frequency and commensurate ratio. In this case, the wave function will almost be restricted to the lowest two instantaneous energy levels. By projecting the wave function to these two relevant states, the dynamics is exactly the same as that for the spin precession dynamics and nutation dynamics around an oscillating axis. We map out the corresponding phase diagram and show that in the low-frequency regime the state is thermalized and in the strong modulation limit, the dynamics is determined by the effective Floquet Hamiltonian. The measurement of these dynamics from the mean position and mean momentum in phase space are also discussed. Our results provide a new thought about the multifrequency resonance in the many-body system.
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