This book is designed primarily to supplement standard texts in elementary Mechanical Vibrations; the statements of theory and principle are sufficiently complete that, with suitable handling of lecture-recitation time, the book could be used as a text by itself. Because of its extensive coverage, graduate students taking further course work in vibrations will lend the last few chapters especially helpful. It should also be of considerable value as a reference book to the practicing engineer. Throughout the book, emphasis is placed on the fundamentals, with discussions and problems extending into many phases and applications of mechanical vibrations. The subject matter is divided into chapters covering duly-recognized areas of theory and study. Each chapter begins with statements of pertinent definitions, principles and theorems. This is followed by graded sets of solved and supplementary problems. The solved problems illustrate and amplify the theory, present methods of analysis, provide practical examples, and bring into sharp focus those fine points which enable the student to apply the basic principles correctly and confidently.