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The model considered in this paper is that of a quarter of anautomobile. The suspension is modeled through a system with one, two, or three degreesof freedom. The springs between the masses in vibratory motion can be linear, nonlinearpolynomial, or nonlinear neo-Hookean. Systems with a single spring (one degree offreedom), two springs (two degrees of freedom), or three springs (three degrees offreedom) are considered, each spring having its own characteristic. The vibrationparameters are determined, and a conclusion is drawn about which type of suspension isthe best from a certain point of view (the amplitudes, speeds, or accelerations of thevibrations). The calculation is developed numerically to determine equilibrium positions,to determine the stability of these equilibrium positions, and to characterize smalloscillations around the stable equilibrium positions. A numerical example illustrates allthe theory presented.