Engineers apply mathematics and science to solve problems. In a traditional undergraduate engineering curriculum, a student begins an academic career by taking courses in mathematics and basic sciences such as chemistry and physics. A student begins to develop problem-solving skills in basic engineering science courses. For a mechanical engineering student, these courses include statics, dynamics, mechanics of solids, fluid mechanics, and thermodynamics. In such courses, students learn to apply basic laws of nature, constitutive equations, and equations of state to develop solutions to abstract engineering problems. Vibrations is one of the first courses where students learn to apply the knowledge obtained from mathematics and basic engineering science courses to solve practical problems. Indeed the problem-solving skills developed in a vibrations course are as valuable as the knowledge of the subject of vibrations. Solution of practical problems in vibrations requires modeling of physical systems. A system is abstracted from its surroundings. Assumptions appropriate to the system are made. Basic engineering science and mathematics are applied to derive a mathematical model. The resulting solution is used to learn about system behavior that could be used in applications such as design. The reader of this text will learn about vibrations by using such a problem-solving approach.