Abstract
The author treats through an approximate method the natural vibrations of the conical coil springs which have the Archimedes' spiral in their planes. The conditions of approximation are shown by two items neglecting the effect of the helical angle and supposing the wire of spring to be fine enough as compared with the radius of the coil, just as in the equation of motion in the natural vibrations of cylindrical coil springs. So a partial differential equation is to be made by the author for the natural vibrations in the direction of coil axis which are produced only by the torsion of a fine spring wire, and to be treated in connection with its solution when the boundary conditions are as follows : (1) both ends are fixed, (2) one end is fixed and the other end free. The results are obtained that the natural frequencies of conical coil springs have been calculated in proportion to the ratio of the small end radius of coil to the large end one, and several forms of the normal mode of vibrations have been shown in both cases respectively.
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