An instantaneous normal mode (INM) analysis of the levitation effect in zeolites is presented in this paper. Lennard-Jones sorbates of variable size and polarizability diffusing in Na-Y zeolite are studied using microcanonical molecular dynamics (MD) simulations. A comparison of the dynamical information from the MD simulations with predictions based on INM analysis shows that the INM spectrum carries several striking signatures of the levitation effect. The fraction of imaginary modes mirrors the trend in the diffusion coefficient as a function of sorbate size and shows an anomalous levitation peak. The Einstein frequency, as a function of sorbate size, shows a minimum at the position of the anomalous peak. The qualitative shape of the INM spectrum changes in the anomalous regime, reflecting the availability of 12-ring window sites for adsorption, in addition to the alpha-cage sites. The velocity autocorrelation functions of the sorbate are well-reproduced from INM data for short time scales of one picosecond, particularly in the anomalous regime. The time of crossover from ballistic to diffusional motion can be approximately predicted from INM spectra since it is found to be similar to the time at which the velocity autocorrelation function first turns negative. These results lead one to expect that the INM spectrum, though an equilibrium static property of the system, can be used very effectively as an indicator of qualitative changes in diffusional dynamics of sorbates in porous media.