The clutching inertia model presents an ideal Bang-Bang control approach, but it is challenging to realize practically through passive means. In this paper, a single-flywheel resettable-inertia damper (SRID) is proposed on the basis of the clutching inertia model. This device is implemented with a rack-and-pinion system, a right-angle gearbox system, and a flywheel-mounted eddy-current damping system. Initially, a mechanical analysis model of this device is established according to its working mechanism. Subsequently, comparative analyses are performed on the performance of SRID in a single degree-of-freedom (SDOF) structure compared to viscous dampers (VDs) subjected to harmonic and seismic excitations. The results show that the SRID can achieve a comparable control effect as VDs with a much smaller need for the damping coefficient, reflecting a damping amplification effect over 100 times. The SRID is effective in controlling peak displacement and absolute acceleration responses, especially for long-period structures. Moreover, the control performance is significantly improved with increasing magnetic induction intensity.