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Ferrimagnets perform versatile properties, attributed to their antiferromagnetic sublattice coupling and finite net magnetization. Despite extensive research, the inhomogeneous dynamics in ferrimagnets, including domain walls and magnons, remain not fully understood. Therefore, we adopted a multi-spin model by considering the effect of the spin torques and explored the localized phase-dependent and inhomogeneous THz-oscillation dynamics in a ferrimagnetic spin-chain. Our results demonstrate that the exchange oscillation mode, induced by spin transfer torque, exhibits three typical phases, and the oscillation frequency is dominated by a joint effective field derived in the spin-chain. We also found that the localized spin configurations can be used to tune the bandwidth and sensitivity of the frequency response. Furthermore, we propose an anti-parallel exchange length to reveal the inhomogeneity in the ferrimagnetic spin-chain, which could serve as a valuable tool for characterizing the spin dynamics of these systems. Our findings offer understandings beyond uniform spin-dynamics in ferrimagnets. Ferrimagnets present advantages over their anitferromagnetic and ferromagnetic counterparts for applications in ultrafast spintronics but the dynamics of the non-uniform spin textures are not as well understood. Here, the authors investigate the inhomogeneous oscillation dynamics in the ferrimagnetic system via a multi-spin model. [ABSTRACT FROM AUTHOR]