In the first approach, experimental dusty plasma structures are often described as systems of parabolically confined particles, interacting by the screened Coulomb potential. On the effect of the confinement, the systems acquire in homogeneity of their structural and dynamical properties. In order to better understand the mechanism of in homogeneity of spectral properties, normal mode analysis of finite system is provided. It is shown that vibrational processes of high frequencies localize in the central region of structure. In the pictures A1-A3 spatial distribution of vibrational amplitude is shown (deeper color means larger amplitude). In the pictures B1-B3 radial profile of vibrational amplitude is shown for illustration. Besides it, in the work, MD simulations are provided to obtain velocity autocorrelation function of every particle in the system. The Fourier transform of VACF can be interpreted as vibrational density of states (VDOS) g(𝜔), which is used to perform averaging of frequency. This is necessary for explanation of the difference between oscillation properties in finite systems in the trap and infinite bulk. To perform an explanation, we divide the finite system into thin rings to obtain ” rings with constant density of particles”.