We consider a two dimensional, time-dependent isotropic harmonic oscillator interacting with a gravitational wave. The frequency of the harmonic oscillator is considered to be time dependent. Making use of the Lewis invariant technique, we compute the Lewis phase for the gravitational wave-detector system when the gravitational wave is carrying plus polarization only. We also consider the gravitational wave to be carrying only the cross polarization and computed the Lewis phase. Finally applying the adiabatic approximation, we calculate the Berry’s geometric phase for the above two cases. This report is based on the publication [1].