In this paper, we present observations of free oscillations of the Earth after major earthquakes in Chile (February 27, 2010, MW8.8) and Japan (March 11, 2011, MW9.1) using data from the dual-sphere superconducting gravimeter (SG - 055), installed at Badargadh (230.47 N, 700.62 E), Kutch, Gujarat, India in March 2009. To see the noise characteristics, we calculated the power spectral density of the gravity time series of 5 quiet days in the frequency band 0.05e20 mHz using the new low noise model (NLNM) as a reference. We compared the noise level of the Badargadh site to other SG sites around the world. This shows that the Badargadh SG is in a low noise state. We find that the noise increases at frequencies below 1 mHz. Such a characteristic is also observed in Djougou (Afrique, Benin) and Strasbourg (France). Using theoretical tides for Gujarat, we estimated a scale factor of about 814 nm/s2/V for Grav1 (lowersphere) and about 775 nm/s2/V for Grav2 (upper-sphere). We corrected the influence of atmospheric pressure from the one-second gravity data before switching to the frequency domain. We extracted a total of 53 Earth's Free Oscillations (EFO) modes during the earthquake in Japan and about 47 EFO modes during the earthquake in Chile. We are able to extract the lowest 0S2 spheroidal mode (0.30945 mHz or 54 min) and 0S0 radial mode (0.81439 mHz or 20 min). The longer time series shows individual 0S2 singlets and 0S3 (0.46855 mHz) singlets due to the Coriolis splitting effect. We cross-referenced the frequencies of these modes using the PREM model and previous global observations. The correlation coefficient between the observed and the PREM model for these two events are 0.999 for Japan earthquake and 0.993 for Chile earthquake. This validates the quality of the data useful for low-frequency studies in seismology. We also calculated the relative deviations of our observed fundamental modes with previously determined observed and theoretical values.We found that the relative deviations of our observed free oscillations do not exceed 0.5%, indicating good correlations.