The dynamic responses to the sinusoidal displacement of a vertical repelling force system with cylindrical type rare-earth magnets are investigated. The analysis is made under an assumption that the repelling force is inversely proportional to the
n-th power of the center distance between the two magnets and is expressed by a series in powers of the relative displacement of the magnets. The results from the numerical calculation and the experiment are concluded as follows:
(1) When the mass is suspended by a repelling force of the magnet on its bottom face, the response curve shows composite characteristics; i. e., the curve changes its form gradually from the soft spring character to the hard spring one with the growth of the amplitude, and the unstable regions are found on both sides of the back-bone curve in the case of subharmonic resonance.
(2) When the mass is interposed between the repelling forces on top and bottom, the response curve takes the hard spring characteristics and the shorter the distance between the fixed magnets, the more remarkable its tendency becomes.
(3) The neutral line of the vibration shifts to the upward direction by a definite degree depending upon the amplitude as well as the unsymmetricity of the repelling forces acting on the vibrating mass.
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