Vibrations of a three-degree-of-freedom wagon system

This paper analyzes the free vibrations of three rigid wagons of equal mass connected by identical elastic elements. The first wagon moves at a constant velocity v, striking and coupling with the second wagon. The system has three degrees of freedom. The three equations of motion were solved analytically. The results of the solution are presented in the figures. Graphs of vibrations, acceleration, and internal forces in the springs are shown.In this paper, we analyze the free vibrations of three rigid wagons of equal mass m connected by identical springs with a constant k. The first wagon moves along a perfectly smooth, horizontal rigid surface at a given velocity v, striking the two remaining coupled, stationary wagons and coupling with the second wagon, as shown in Figure 1. The system undergoes free vibrations. In this report, we will derive the three equations of motion for this system, which has three degrees of freedom.
We will determine the vibrations of the three generalized coordinates q1(t), q2(t), q3(t) by applying an analytical solution to the three linear equations of motion. (…)

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