With numerical calculation of coupled Bloch equations, we have simulated the spin dynamics of nuclear magnetic resonance gyroscope based on alkali metal-noble gas hybrid trispin system. From the perspective of damping harmonic oscillator, a thorough analysis of the response dynamics is demonstrated. The simulation results shows a linear increasing response of gyroscope signal while the noblge gas nuclear spin magnetization and alkali atomic spin lifetime parameters are at the over damping condition. An upper limit of response is imposed on the NMR gyroscope signal due to the inherent dynamics of the hybrid trispin system. The results agrees with present available experimental results and provide useful guidings for future experiments.
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