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The Fifth Edition of this classic work retains the most useful portions of Timoshenkoa s book on vibration theory and introduces powerful, modern computational techniques. The normal mode method is emphasized for linear multi--degree and infinite--degree--of--freedom systems and numerical methods dominate the approach to nonlinear systems. A new chapter on the finite--element method serves to show how any continuous system can be discretized for the purpose of simplifying the analysis. Includes revised problems, examples of applications and computer programs.