Dynamical problems about energy dissipation in a finite multi-degree of freedom Hamiltonian system are studied. The energy dissipation in the relevant system is realized by numerical simulation. By employing power spectrum analysis on q(t) or p(t) of the motion in the relevant system, it is found that during the dissipative process, distribution of the power spectral density about the motion extends to both lower and higher frequencies. The more irrelevant degrees of freedom are, the broader the distribution extends. Higher frequencies decrease as time evolves but there are no remarkable changes for lower frequency components.