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Originally published in 1960, the primary aim of this book was to give the reader an insight into the vibration characteristics of a machine or structure rather than to present them with a recipe for formal calculations. Within the text classical theory is developed by starting from the concept of steady forced motion and then introducing free motion as a limiting case. The concept of resistance or 'dynamic flexibility' is used throughout and provides a link between the treatment of very simple systems, multi-freedom systems with lumped parameters and infinite-freedom systems. It also provides a tool for breaking down complex problems into simpler parts. The mathematics will be understood by a student taking an honors course in engineering, and the book's primary purpose was to provide them with a background for their studies and with a path along which to advance for further work.