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The switching on/off system, which is one of the means to control the semi-active damper, is utilized with the merit of its simple control method but the shock force occuring in the mode change is still a problem to be overcome in this kind of damper. In this study, by simulating a quarter car model which incorporates the damper mass and the stiffness of damper mount bushes, the presence of the shock force and the characteristic of the shock force was examined. This study suggests an interesting relationship between the frequency of the shock force induced in the damper mode change and the stiffness of the damper mount bushes.