Dynamics of dissipation local vibrations to the surrounding substrate is a key issue in friction between sliding surfaces as well as in boundary lubrication. We consider a model system consisting of an excited nano-particle which is weakly coupled with a substrate. Using three different methods, we solve the dynamics of energy dissipation for different types of coupling between the nanoparticle and the substrate, where different types of dimensionality and phonon densities of states were also considered for the substrate. In this paper, we present a microscopic analysis of transient properties of energy dissipation via phonon discharge toward the substrate. Finally, important conclusions of our theoretical analysis are verified by a realistic study, where the phonon modes and interaction parameters involved in the energy dissipation from an excited benzene molecule to the graphene are calculated by using first-principles methods. The methods used are applicable also to dissipative processes in the contexts of infrared Raman spectroscopy and atomic force microscopy of molecules on surfaces.