The forced vibration probjlem of a finite sphere with an exciting source embedded inside it was treated. The source is assumed to oscillate sinusoidally and the complex dilatational modulus is used to describe the motion inside the sphere. If the outer surface of the sphere is restrained from radial displacement, the ratio of the amplitude of a mid-point to the amplitude of a point on the exciting source could be used as an indication of the dilatational properties of the sphere. From the criterion of maximum amplitude ratio in conjunction with the frequency, the dilatational properties of a testing material can be determined. This method can be applied to visco-elastic fluids as well as solids. (Author).

The technique of forced vibration has been applied to the study of the properties of viscoelastic materials. It is found, through the analysis of a free sphere with a harmonic oscillating internal source, that the vibration amplitude ratio of two measuring points is associated with the complex dilatational constants and the complex ratio of the material, a quantity directly related to the complex Poisson's ratio. Therefore, from the criterion of maximum amplitude ratio (i.e. by adjusting the frequency of the source until the amplitude ratio reaches maximum), these properties can be expressed in terms of the amplitude ratios and their frequencies. For the convenience of laboratory testing, two particular amplitude ratios, in conjunction with their frequencies, have been employed for this purpose. Simple expressions are given, relating the properties of the test material to quantities measurable in the laboratory, namely the maximum amplitude ratios and their corresponding frequencies. (Author).