There are many studies that present mathematical models of a system’s response to excitation by a random sequence of impulses, but none of these models has been experimentally verified. This article presents a study investigating the discrepancies between a mathematical model, which includes the Dirac delta, and the actual dynamic response of an RLC system. The model describes vibrations in a discrete system subjected to a stochastic sequence of impulses. The system parameters were identified using an algorithm based on statistical analyses such as interval and point estimation, nonlinear curve fitting to experimental data, and analysis of fitting errors. The research showed that, system's response to individual impulses depends on both the value of the impulse and its distribution, resulting in dynamic variations of system parameters. Furthermore, a signal flattening effect is observed, which significantly influences the vibrational output characteristics. The results indicate that identifying the underlying impulse distribution will require the application of artificial intelligence algorithms based on image analysis. This approach gives hope for high effectiveness, particularly in the case of low-intensity impulses occurring in a random temporal sequence.