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Review by for Rating: I recently used this as a text to teach Vibrations to Mechanical Engineering seinors after Vibration Analysis by Vierck went out of print. I was attracted to Rao's book because much of the presentation is similar to Vierck. After using this text for one semester, I was not satisfied. I was particularly concerned by Chapter 2 where the fundamentals of damped single degree of freedom systems are covered. This Chapter is critical to building the foundation of Vibration Theory and I was disturbed to find that two critical plots, the time history comparison of responses with various damping levels and the phase plane plot for the same cases were seriously incorrect. While errors always can be found in texts, these plots were so obviously wrong at first glance that I wondered how a book with 29 reviewers (as listed in the Acknowledgements) has such glaring errors. As I progressed through the text I found a number of other errors including incorrect equations in some places. I also found that some material, emphasized in Vierck, that I consider important was buried in the worked examples rather than being emphasized as part of the book's text. While the book does present a lot of material and gives some interesting problems, I found that I was not comfortable with the text at the end of the course. I have since decided to drop this book from consideration as our text.