THE ROLE OF DIFFERENTIAL EQUATIONS IN ANALYZING DYNAMIC PROCESSES IN MECHANICAL ENGINEERING.

Authors

  • Khamdamova Dilnoza Rahmatilla kizi Assistant of the Department of “Technological Machines and Labor Protection” Andijan State Technical Institute

Keywords:

Differential equations, mechanical engineering, dynamic systems, vibration damping, mathematical modeling, resonance, damping coefficient.

Abstract

 This article explores the application of mathematical modeling, specifically ordinary differential equations (ODEs), in the analysis of dynamic systems within mechanical engineering. The study focuses on the vibration damping of machine components and the stability of mechanical structures under periodic external forces. By utilizing second-order linear differential equations, a model for a spring-mass-damper system is developed. The results demonstrate how varying damping coefficients affect the kinetic energy dissipation and structural integrity of mechanical parts. The findings provide a theoretical foundation for improving the wear resistance and operational safety of industrial machinery.

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References

Boyce, W. E., DiPrima, R. C., & Meade, D. B. (2017). Elementary Differential Equations and Boundary Value Problems. Wiley.

Rao, S. S. (2011). Mechanical Vibrations. 5th Edition, Prentice Hall.

Zill, D. G. (2012). A First Course in Differential Equations with Modeling Applications. Cengage Learning.

Inman, D. J. (2014). Engineering Vibration. Pearson.

Timoshenko, S. (1937). Vibration Problems in Engineering. D. Van Nostrand Company.

Azlarov, T., & Mansurov, H. (2005). Mathematical Analysis. Toshkent: O‘qituvchi.

Yuldashev, S. U., & Mamadaliyev, M. A. (2020). Modelling of Wear Processes in Agricultural Machinery Components. Journal of Engineering and Material Science.

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Published

2026-05-05

How to Cite

Khamdamova Dilnoza Rahmatilla kizi. (2026). THE ROLE OF DIFFERENTIAL EQUATIONS IN ANALYZING DYNAMIC PROCESSES IN MECHANICAL ENGINEERING. Journal of Applied Science and Social Science, 16(5), 130–135. Retrieved from https://www.internationaljournal.co.in/index.php/jasass/article/view/4276

Issue

Vol. 16 No. 5 (2026): Journal of Applied Science and Social Science

Section

Articles

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