This article studies the fundamental concepts of harmonic and mechanical vibrations, their nature, and practical applications. Harmonic vibrations are oscillations that repeat sinusoidally over time, maintaining constant amplitude and frequency during energy exchange processes. They are widely used in mechanical systems, especially in simplified models such as the mass-spring system. Mechanical vibrations refer to the motion of bodies caused by external forces or their inertia. The article covers the mathematical modeling of vibrations, energy transfer, and types of vibrations — free, forced, and damped. Furthermore, methods for controlling mechanical vibrations and reducing their effects in practice are discussed. The significance of harmonic and mechanical vibrations in engineering, physics, and technology, along with their applications across various fields, is also highlighted. This research provides essential knowledge for the effective management and analysis of vibrations in mechanical systems.

harmonic vibrations, mechanical vibrations, free vibration, forced vibration, damped vibration, sinusoidal motion, energy exchange, mechanical systems, vibration modeling, amplitude, frequency, vibration control.

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