The book "Mechanical Vibrations: An Introduction" is authored by György Szeidl and László Péter Kiss, both from the Institute of Applied Mechanics at the University of Miskolc in Hungary. The book is designed as a textbook for M.Sc. students in mechanical engineering, particularly those who may have varying levels of prior knowledge in tensor algebra and analysis. To accommodate this, the authors have structured the content to be accessible to a broad audience, with a focus on matrix notation to avoid the complexities of tensorial notation. The book is divided into ten chapters, each covering different aspects of mechanical vibrations. Chapter 1 serves as an introduction to the fundamentals of dynamics, including kinematic relations and the principles of kinetics. Chapter 2 discusses impact, both central and eccentric, with graphical solutions and Maxwell’s diagrams. Chapter 3 introduces single-degree-of-freedom systems, covering undamped and damped free vibrations, forced vibrations, and machine foundation problems. Chapter 4 provides an introduction to multidegree-of-freedom systems, using Lagrange’s equations of motion and focusing on spring-mass systems. Chapter 5 delves into the general theory of multidegree-of-freedom systems, eigenvalue problems, and forced vibrations. Chapter 6 covers special problems of rotational motion, such as flywheels and balancing. Chapter 7 addresses systems with infinite degrees of freedom, including longitudinal, transverse, and flexural vibrations of beams and rods. Chapter 8 and 9 focus on eigenvalue problems of ordinary differential equations and systems, respectively, with detailed solutions and numerical examples. Chapter 10 discusses eigenvalue problems described by degenerated systems of ordinary differential equations, specifically for curved beams. The book includes appendices that provide a brief introduction to tensor algebra, useful relationships, and solutions to selected problems. The authors acknowledge the contributions of Dr. Gábor Csernák, Mrs. Sudhany Karthick, and several individuals who provided valuable assistance in preparing the manuscript. The book aims to provide a comprehensive and practical guide to mechanical vibrations, suitable for both students and professionals in the field.The book "Mechanical Vibrations: An Introduction" is authored by György Szeidl and László Péter Kiss, both from the Institute of Applied Mechanics at the University of Miskolc in Hungary. The book is designed as a textbook for M.Sc. students in mechanical engineering, particularly those who may have varying levels of prior knowledge in tensor algebra and analysis. To accommodate this, the authors have structured the content to be accessible to a broad audience, with a focus on matrix notation to avoid the complexities of tensorial notation. The book is divided into ten chapters, each covering different aspects of mechanical vibrations. Chapter 1 serves as an introduction to the fundamentals of dynamics, including kinematic relations and the principles of kinetics. Chapter 2 discusses impact, both central and eccentric, with graphical solutions and Maxwell’s diagrams. Chapter 3 introduces single-degree-of-freedom systems, covering undamped and damped free vibrations, forced vibrations, and machine foundation problems. Chapter 4 provides an introduction to multidegree-of-freedom systems, using Lagrange’s equations of motion and focusing on spring-mass systems. Chapter 5 delves into the general theory of multidegree-of-freedom systems, eigenvalue problems, and forced vibrations. Chapter 6 covers special problems of rotational motion, such as flywheels and balancing. Chapter 7 addresses systems with infinite degrees of freedom, including longitudinal, transverse, and flexural vibrations of beams and rods. Chapter 8 and 9 focus on eigenvalue problems of ordinary differential equations and systems, respectively, with detailed solutions and numerical examples. Chapter 10 discusses eigenvalue problems described by degenerated systems of ordinary differential equations, specifically for curved beams. The book includes appendices that provide a brief introduction to tensor algebra, useful relationships, and solutions to selected problems. The authors acknowledge the contributions of Dr. Gábor Csernák, Mrs. Sudhany Karthick, and several individuals who provided valuable assistance in preparing the manuscript. The book aims to provide a comprehensive and practical guide to mechanical vibrations, suitable for both students and professionals in the field.