Coherent interaction of a monochromatic gravitational wave with both elastic bodies and electromagnetic circuits

The interaction of a gravitational wave with a system made of an RLC circuit forming one end of a mechanical harmonic oscillator is investigated. We show that, in some configurations, the coherent interaction of the wave with both the mechanical oscillator and the RLC circuit gives rise to a mechanical quality factor increase of the electromagnetic signal. When this system is used as an amplifier of gravitational periodic signals in the frequency range 50-1000 Hz, at ultracryogenic temperatures and for sufficiently long integration times (up to 4 months), a sensitivity of 10^(-24)-10^(-27) on the amplitude of the metric could be achieved when thermal noise, shot noise and amplifier back--action are considered.