Response of a mechanical oscillator to a gravitational wave.

The conventional treatment [J. Weber, General Relativity and Gravitational Waves (Interscience, New York, 1961)] of an undamped mass quadrupole oscillator driven by a gravitational wave assumes the excitation force to be that exerted by the wave on the mass. The force exerted by the wave on the spring has heretofore been ignored. I have calculated this latter force Fs driving the spring and discovered that it is related to the force Fm driving the mass; thus, <DFORMULA>F_m = ω₀^-2 <FRACTION><NUM>d²</NUM><DEN>dt²</DEN></FRACTION> F_s</DFORMULA>, in which ω0 is the resonant circular frequency of the oscillator. The total driving force is the sum Fm + Fs. This total force is incapable of exciting the normal mode of the oscillator, thus supporting my earlier conjecture [P. J. Westervelt, Soviet Phys. JETP Letters 4, 225 (1966), Footnote 4] that passive detectors of gravitational waves cannot be realized in principle. Active detectors, i.e., generators of gravitational waves, can measure radiation from another source. [ABSTRACT FROM AUTHOR]