The investigation on the temporal dynamics of graphene-wrapped core–shell nanoparticles under the illumination of a Gaussian impulse have been carried out. By altering the graphene layers and the aspect ratio of the core–shell structure, we can adjust the resonant modes into typical cases in regime of terahertz. Accordingly, different scenarios for the temporal evolution are detected, which include two kinds of ultrafast oscillation with exponential decay tendency, pure exponential decay, and Gaussian shape, when the pulse duration of the incident pulse is much shorter than, similar to, and much longer than the localized surface plasmon lifetime. To one's interest, when the coupling between two resonant modes exists, one predicts the long-periodic oscillation, whose period is just the difference between the frequencies of the resonant modes. Hence, the intrinsic properties of the ultrafast oscillation can be hardly influenced by the input signals. Further quantitative calculation demonstrate that the periods of the ultrafast oscillations can be tuned by different physical mechanisms, which are, respectively, based on the self-interacting correction of a single resonance and the strong coupling between the resonant modes in frequency domain. Our results may be applicable in the fields of optical sensors, optical information processing, and other nanophotonic devices.