Most engineering systems are continuous and have an infinite number of degrees of freedom. The analysis of a multi-degree-of-freedom system is introduced. For simplicity of analysis, continuous systems are often approximated as multi-degree-of-freedom systems. All the concepts introduced in the preceding chapter can be directly extended to the case of multi-degree-of-freedom systems. There is one equation of motion for each degree of freedom; if generalized coordinates are used, there is one generalized coordinate for each degree of freedom. The equations of motion can be obtained from Newton s second law of motion or by using the influence coefficients defined in Sect. 6.4. It is introduced to derive the equations of motion of a multi-degree-of-freedom system by using Lagrange s equations.