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The eddy current and force distribution on the plunger of a single-stage induction damper is analyzed for the numerical investigation and design improvement of induction dampers. A 3-D finite-element method is applied to the eddy current analysis of the magnetic field, and the Lorentz force on the plunger is calculated using the nodal force method. The simulation results show that the Lorentz force on the plunger can be increased by installing a ferromagnetic enclosure around the coil. Furthermore, an induction damper model is proposed considering the skin effect of eddy current on the plunger. The results show that the flux interlinking the plunger is increased by reducing the thickness of the plunger. Finally, the dynamic simulation is carried out to verify the design and investigate the dynamic characteristics of the induction damper. The damper with a ferromagnetic groove enclosing the coil is proven to be more effective.