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