The course begins with an introduction to vibrations, defining fundamental concepts and highlighting their importance in various fields. It continues with the study of free, undamped linear oscillations, analyzing periodic motions and the equations of motion that describe them. Next, the course addresses free, damped linear oscillations, emphasizing the concepts of damping and energy dissipation, as well as their impact on system behavior.

Forced oscillations are then explored, focusing on the response of systems to external excitation and the phenomena of resonance. The course proceeds to mechanical waves, examining different types of waves and detailing their fundamental properties, while establishing a connection between vibrations and waves. Special attention is given to longitudinal waves in fluids, studying their propagation and defining characteristics.

The analysis of waves in solids follows, discussing the mechanical properties that influence wave transmission. The final section is dedicated to the study of transverse waves in a string, highlighting fundamental mechanical principles through rigorous modeling and practical applications. The synthesis of concepts underscores the significance of waves and vibrations in both physics and technology.