Palm takes the reader into a systematic exposition of the theory of mechanical vibrations. Showing how this can be understood in terms of the basic physics. He walks through progressively more intricate cases, starting with the simplest of systems with 1 degree of freedom.
The book is positioned as a text for an undergrad course, with numerous problem sets and chapter summaries. Also, he chooses Matlab in order to give numerical methods that can be applied to various problems.
By the way, Palm is also the author of a book on using Matlab, "Introduction to Matlab 7 for Engineers". You might want to also check that out, if you are considering using Matlab as your numerical engine.
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