ABSTRACT
As in the case of a single-degree-of-freedom system, a system with multiple degrees of freedom will vibrate even without the presence of an external force whenever it is subjected to disturbances in the form of initial displacements, or initial velocities, or both, along one or more of its degrees of freedom. The free vibrations of a multidegree-of-freedom system are governed by the following equations of motion
Mu¨+ Cu˙+ Ku = 0 (10.1) where, as usual, M is the mass matrix, C the viscous damping matrix, K the stiffness matrix, and u the displacement vector.
