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The general theory of time-dependent frequency and time-dependent mass('effective mass') is described.The general theory for time-dependent harmonic-oscillator is applied in the present research for studying certain quantumeffects in the interferometers for detecting gravitational waves.When anastronomical binary system approaches its point of coalescence thegravitational wave intensity and frequency are increasing and this can lead tostrong deviations from the simple description of harmonic-oscillations for theinterferometric masses on which the mirrors are placed.It is shown that undersuch condtions the harmonic-oscillations of these masses can be described bymechanical harmonic-oscillators with time-dependent frequency andeffective-mass. In the present theoretical model the effective-mass isdecreasing with time describing pumping phenomena in which the oscillatoramplitude is increasing with time . The quantization of this system is analyzedby the use of the adiabatic approximation. It is found that the increase of thegravitational wave intensity, within the adiabatic approximation, leads tosqueezing phenomena where the quantum noise in one quadrature is increased andin the other quadrature is decreased.

Harmonic oscillator with time-dependent effective-mass and frequency  with a possible application to 'chirped tidal' gravitational waves forces  affecting interferometric detectors