The main aim of the present paper is the evaluation of the effects of the instrumental energy resolution on the mean square displacement (MSD) obtained by elastic incoherent neutron scattering (EINS). In particular, this study is performed in the time domain, through the time-Fourier transform of the elastically scattered neutron intensity, and is mainly focused on the connection between the system MSD and the measured MSD. It is shown how in the case of EINS, the instrumental energy resolution gives rise to the time integration of the time-dependent system MSD function weighted in time by the resolution function. The formulated approach is applied to the data collected on dry and hydrated (H2O and D2O with h = 0.4) lysozyme samples by two spectrometers working with a different instrumental resolution (the IN10 and IN13 spectrometers of the Institute Laue-Langevin). As a result, the procedure furnishes an excellent agreement for the system MSD evaluated in the low temperature range up to T = 40 K.