Multiple DegreeofFreedom Example 
Consider the 3 degreeoffreedom system,
There are 3 degrees of freedom in this problem since to fully characterize the system we must know the positions of the three masses (x_{1}, x_{2}, and x_{3}). Three free body diagrams are needed to form the equations of motion. However, it is also possible to form the coefficient matrices directly, since each parameter in a massdashpotspring system has a very distinguishable role. 
Equations of Motion from Free Body Diagrams 
The equations of motion can be obtained from free body diagrams, based on the Newton's second law of motion, F = m*a.
The equations of motion can therefore be expressed as,
In matrix form the equations become,

Equations of Motion from Direct Matrix Formation  
Observing the above coefficient matrices, we found that all diagonal terms are positive and contain terms that are directly attached to the corresponding elements. Furthemore, all nondiagonal terms are negative and symmetric. They are symmetric since they are attached to two elements and the effects are the same in these two elements (a condition known as Maxwell's Reciprocity Therorem). They are negative due to the relative displacements/velocities of the two attached elements. In summary,  
