We recalled the model of a suspension mechanism, interpreting the constants zeta and omega[n]. See the Maple worksheet:
Then we consider nonhomogeneous ODEs and showed how every higher-order differential equation can be written as a system of first-order differential equations, using auxiliary variables. The eigenvalues of the matrix of the system are the roots of the characteristic equation of the original differential equation: We elaborated the multiple spring-mass system and derived a model for traffic on the highway.