Vibrations and Sound: Multiple Degree of Freedom Systems

Up to now, all of the systems that we have considered have been single degree of freedom systems for which one coordinate is sufficient to completely specify the configuration of the system. While there are numerous systems that can be reasonably modeled as having a single degree of freedom, there are many other systems that require a more detailed model. Discrete vibrating systems are classified as either single degree of freedom (SDOF) or multiple degree of freedom (MDOF) systems. There are many parallels between single and multiple degree of freedom systems. We will begin our discussion of MDOF systems by considering two degree of freedom (TDOF) systems which are the simplest. This will help to illustrate of the important features of MDOF systems while keeping the development as simple as possible. Once the two degree of freedom system is understood, extensions to systems with more degrees of freedom is straightforward.