ANALYSIS OF PENDULUM MOTION USING DIFFERENTIAL EQUATIONS AND A MATHEMATICAL SOFTWARE PACKAGE
Abstract
In this article, the oscillatory motion of physical and mathematical pendulums is studied based on mathematical modeling. Initially, the physical structure of each pendulum, the forces causing their oscillations, and their mechanical properties are analyzed, and the motion process is expressed in the form of differential equations. Newton's second law and fundamental physical principles are employed in deriving the motion equations. The analyses conducted in the article aim to highlight the theoretical and practical significance of differential equations derived from physical models. Through this, a deeper understanding of pendulum motion is achieved, along with possibilities for applying it to real physical systems and using it as an educational tool in modern learning processes. The theoretical and practical results obtained in the article illustrate the role of differential equations in modeling physical problems and justify the effectiveness of using mathematical software packages in solving them. Moreover, these methods and results are important for their effective use in teaching mechanics courses and organizing laboratory work in higher education.
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