In recent year, progress has been made in the study of ballistic heat flow and phonon scattering by phonon spectroscopy and phonon-imaging techniques. Regarding the femtosecond laser application to nanostructures, phonon generation in nanoscale electronics is the focus of interest in the investigation of the mechanism of thermal wave formation at different heating pulses and conditions for heat flux propagation in nanostructures. We test an atomic model of thermal transport in a nanoribbon after a few picosecond pulse heating that leads to the simultaneous presence of two modes, namely, coherent phonons and diffusion, by molecular dynamics (MD) simulation. Our main goal is to investigate the characteristics of the highest magnitude vibrational motion of wave front atoms at different heating pulses and ascertain their correspondence to a single longitudinal optical phonon. To this end it is shown that in the MD model, the equations of heat flux taken through the boundaries of a corresponding sampling area can resolve coherent phonon motion with high resolution when translational and vibrational modes are evaluated separately. Such a definition of heat flux allows the tracing of formation and dynamics of a single phonon. It is applied for different times of heating of a nanoribbon sample. The mechanism underlying the decay of phonons into diffusion is also probed, and energy conversion over the nanoribbon is evaluated. The relevant size of the area for the temporal and spatial flux resolution of a coherent phonon in the MD model is confirmed.