These pages give a brief introduction to the use of eigenvalues and eigenvectors to study vibrating systems for systems with no inputs. MatLab code is also included on the "Vibrating Systems" page.
Analyzing a system in terms of its eigenvalues and eigenvectors greatly simplifies system analysis, and gives important insight into system behavior. For example, once the eigenvalues and eigenvectors of the system above have been determined, its motion can be completely determined simply by knowing the initial conditions and solving one set of algebraic equations.
Before you begin, you should be familiar with matrix fundamentals (notation, addition, multiplication, inversion, solving sets of linear equations...)