  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 quantum
effects in the interferometers for detecting gravitational waves.When an
astronomical binary system approaches its point of coalescence the
gravitational wave intensity and frequency are increasing and this can lead to
strong deviations from the simple description of harmonic-oscillations for the
interferometric masses on which the mirrors are placed.It is shown that under
such condtions the harmonic-oscillations of these masses can be described by
mechanical harmonic-oscillators with time-dependent frequency and
effective-mass. In the present theoretical model the effective-mass is
decreasing with time describing pumping phenomena in which the oscillator
amplitude is increasing with time . The quantization of this system is analyzed
by the use of the adiabatic approximation. It is found that the increase of the
gravitational wave intensity, within the adiabatic approximation, leads to
squeezing phenomena where the quantum noise in one quadrature is increased and
in the other quadrature is decreased.
