In this paper, we adopt an approach suitable for monitoring the time evolution of the intramolecular contribution to the spectral density of a set of identical chromophores embedded in their respective environments. We apply the proposed method to the Fenna-Matthews-Olson (FMO) complex, with the objective to quantify the differences among site-dependent spectral densities and the impact of such differences on the exciton dynamics of the system. Our approach takes advantage of the vertical gradient approximation to reduce the computational demands of the normal modes analysis. We show that the region of the spectral density that is believed to strongly influence the exciton dynamics changes significantly in the timescale of tens of nanoseconds. We then studied the impact of the intramolecular vibrations on the exciton dynamics by considering a model of FMO in a vibronic basis and neglecting the interaction with the environment to isolate the role of the intramolecular exciton-vibration coupling. In agreement with the assumptions in the literature, we demonstrate that high frequency modes at energy much larger than the excitonic energy splitting have negligible influence on exciton dynamics despite the large exciton vibration coupling. We also find that the impact of including the site-dependent spectral densities on exciton dynamics is not very significant, indicating that it may be acceptable to apply the same spectral density on all sites. However, care needs to be taken for the description of the exciton-vibrational coupling in the low frequency part of intramolecular modes because exciton dynamics is more susceptible to low frequency modes despite their small Huang-Rhys factors.