Linear Oscillations in Conservative Systems

The textbook presents a systematic exposition of the fundamentals of the theory of mechanical oscillations without energy dissipation, using mathematical tools accessible to first-year students of higher education institutions. It examines in detail free oscillations of the harmonic oscillator, energy characteristics and phase trajectories, various types of pendulums, as well as the principles of superposition of harmonic oscillations and their vector representation. Special attention is given to the analysis of forced oscillations and the phenomenon of resonance. The final chapters address more complex cases, including the motion of a particle under the action of a repulsive force from a force center and the behavior of mathematical and physical pendulums at large deviations from the equilibrium position.

The textbook is intended for students of bachelor’s and master’s programs in engineering and natural sciences who study general physics, as well as for postgraduate students seeking to deepen their knowledge in the field of oscillation theory. In addition, it will be useful for instructors teaching courses in theoretical physics, applied mechanics, engineering dynamics, and related disciplines, as well as for anyone interested in gaining a deeper understanding of the fundamental laws governing oscillatory processes in natural and technical systems.