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Exact solutions of the equation for the free torsional oscillations of an inhomogeneous sphere

SEISMOLOGICAL OBSERVATORY INDIA METEOROLOGICAL DEPARTMENT, LODI ROAD, NEW DELHI—3, India

Abstract

The equation of motion of free torsional oscillations of an inhomogeneous sphere where the modulus of rigidity and density are functions of distance from the center of the sphere is considered. A systematic method is developed to obtain the inhomogeneity for which the equation can be solved in terms of hypergeometric, Whittaker and Bessel functions. A few simple inhomogeneities yielding exact solutions in terms of these functions are presented.

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