This book presents the fundamental concepts of modeling and analysis of vibrations in mechanical systems with one or more degrees of freedom. The presentation of classic topics is enriched by discussions on equilibrium, stability, and the linearization of the equations of motion. Practical examples throughout the text illustrate the applicability of the theory and explore the physics behind the equations. This book includes various Matlab codes, which allow readers to modify parameters and investigate the behavior of a wide range of mechanical systems. Furthermore, it is demonstrated how some of the mechanical systems studied can be constructed using ordinary materials, enabling readers to compare the theoretical results predicted by the mathematical models with the actual observed behavior.