Final isolation stage for a spherical gravitational wave antenna

In order to measure the very weak interaction between a gravitational wave and a resonant-mass detector the antenna must be vibrationally isolated from all external excitations. In this article we describe an analytical and experimental study of the final support to a spherical antenna. We derive an analytical procedure for optimizing the dimensions of the support for maximum attenuation. The results of a finite element analysis are also presented that takes into account the elasticity of the sphere. The described techniques were used for designing the final support of a room-temperature prototype antenna. We found the measurements on this system to be in good agreement with the expected transfer functions.