A novel magnetic damper, named the MS-damper, was developed based on a newly discovered energy conversion method, by which mechanical vibratory energy is converted to electromagnetic energy. The structure of the MS-damper is based on a magnetic seesawing effect or the oscillation-induced portioning out of flux from a permanent magnet. This paper discusses damper principles, followed by an outline of analyses on damping forces using Bessel-Kelvin functions. Frequency characteristics of damping coefficients are introduced as well. Test results which show good agreement with analytical results are discussed as well. All in all, the damping coefficients obtained from the test results were ten-times larger than the most favorable coefficients obtained from conventional dampers.