## 2 Methodology
The influence of the number of terms in polynomial (23), which approximates block \(\Phi_{0}\), can be assessed by comparing the data in the fourth row of Table 2 with those in the fifth row, which presents the results of integrating system (47), with \(b_{n}=0\) and parameters \(a_{n}\) taken from the sixth row of Table 1. The transition from a fourth-degree polynomial (23) to a second-degree polynomial has practically no effect on the results (the error does not exceed 1.3%). Thus, a second-degree polynomial can be used to approximate block \(\Phi_{0}\). The fifth case was also calculated for viscous friction dampers (sixth row); the forces, \(S\) and \(S_{B}\), were found to be smaller with viscous damping across the entire speed range considered. If we compare the results given in the second and sixth rows of Table 2--that is, results obtained for the same problem but solved using different approaches (in the frequency domain--second case; and in the time domain with prior approximation of block \(\Phi_{0}\) by a second-degree polynomial--sixth case), we observe a very good match (only in one case does the discrepancy reach 6%, while in all others, it is significantly smaller). In all subsequent cases (rows 7-11), the influence of the adjacent wheelset is not taken into account, and the block \(\Phi_{0}\) is approximated by a second-degree polynomial, meaning that the given track parameters are considered. The seventh, eighth, and ninth cases correspond to the same-numbered cases in Table 1. In the seventh and eighth cases, \(m_{re}\) and \(K_{re}\) were calculated based on the equality of the kinetic and potential energies of the distributed and reduced systems. However, in the seventh case, track damping was overestimated. The high damping value led to a noticeable decrease in the magnitude of all forces at high speeds (compared to the second case: the suspension forces decreased by up to 19%, and the interaction forces by up to 31% at a speed of 180 km/h). Without considering damping in the beam (eighth case), the forces are close to those obtained from the continuous model without accounting for the influence of adjacent wheelsets (second case). In the ninth case, the results are given for the equivalent parameters obtained by comparing the frequency characteristics of the distributed and discrete systems. The differences from the eighth case are minor: at a speed of 180 km/h, the forces, \(S\), decreased by 4%, and \(S_{B}\) by 7%. Therefore, all the considered methods of reducing the distributed track parameters to lumped parameters yield similar results in terms of the magnitude of the forces acting on the wagon body and wheelsets, except in cases with excessively high friction. In the last two cases, the tenth and eleventh, the influence of the inertial properties of the track on the considered dynamic characteristics of the railcar is investigated. In case 10, the parameters from case 9 are used, but \(m_{re}\) is assumed to be zero. The forces in the suspension system change insignificantly (by no more than 6%), while the interaction forces for the non-inertial track are 8% higher than those for the inertial track (at speeds of \(C=\)140-180 km/h). Finally, let us compare cases 5 and 11, which allow us to assess the impact of the inertial properties of the track when Coulomb friction dampers are used in the railcar's suspension system. The forces, \(S\), vary less in this case (differences do not exceed 8%), as in the linear problem, compared to the interaction forces, which increase sharply for the non-inertial track (from 21% at \(C=\) 60 km/h to 96% at \(C=\) 180 km/h). This leads to the conclusion that it is essential to take into account the inertial properties of the track, especially when analyzing railcar vibrations in a nonlinear setting.