The dynamic process of the railway track–rolling stock interaction is characterized by time-dependent dynamics that are determined by both the varying characteristics of the interaction objects and the varying climatic conditions. This study investigated the effect of different groups of influence on the dynamic process, with a view towards the reduction of the cases of randomness during the registration of the process in experiments and an expansion of the understanding of the processes happening during the assessment of the registered data. The static nature of the rolling stock has been demonstrated to be not uniform and to influence the scattering of dynamic values under the variation of vertical and horizontal forces due to the characteristics of a rolling stock. The position of the rolling stock truck relative to the track axis during the movement of the rolling stock has been shown to enhance static non-uniformity. The results of the longitudinal force measurements under the three-point and Schlumpf methods have suggested that it is necessary to investigate the process of rail warping under the action of the rolling stock wheels. To enhance the output of the experiments, it is proposed to consider not only the stiffness of the basis of the oscillatory processes that imitate the physical process of oscillation of the system elements by means of the oscillation amplitude, but also the time of response to the oscillation process by using and assessing the triggering time rather than the frequencies of the oscillation processes.