title: Simplified Handbook of Vibration Analysis, Vol. 1
author:  Art Crawford 
description: Introduction to Vibration System Response Transducers General Analysis Techniques Phase Field Balancing Shaft Alignment
zlib_text: CHAPTER 28, PART I
  MATRIX METHODS 
  OF ANALYSIS
  Stephen H. Crandall
  Robert B. McCalley, Jr.
  INTRODUCTION
  The mathematical language which is most convenient for analyzing multiple degree-
  of-freedom vibratory systems is that of matrices. Matrix notation simplifies the pre-
  liminary analytical study, and in situations where particular numerical answers are
  required, matrices provide a standardized format for organizing the data and the
  computations. Computations with matrices can be carried out by hand or by digital
  computers. The availability of programs such as MATLAB makes the solution of
  many complex problems in vibration analysis a matter of routine.
  This chapter describes how matrices are used in vibration analysis. It begins with
  definitions and rules for operating with matrices.The formulation of vibration prob-
  lems in matrix notation then is treated. This is followed by general matrix solutions
  of several important types of vibration problems, including free and forced vibra-
  ti