  We apply the standard theory of the elastic body to obtain a set of equations
describing the behavior of an acoustic Gravitational Wave detector, fully
taking into account the 3-dimensional properties of the mass, the readout and
the signal. We show that the advantages given by a Dual detector made by two
nested oscillators can also be obtained by monitoring two different acoustic
modes of the same oscillator, thus easing the detector realization. We apply
these concepts and by means of an optimization process we derive the main
figures of such a single-mass Dual detector designed specifically for the
frequency interval 2-5kHz. Finally we calculate the SQL sensitivity of this
detector.
