Vibrations and Mechanical Waves
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Date
2024-11-18
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University of M'sila
Abstract
This course handout, Vibrations and Mechanical Waves, is designed to align with the LMD-S3
License training curriculum in the fields of Material Science (SM) and Science and Technology
(ST). The content is structured into two parts, providing a comprehensive exploration of vibrations
and wave propagation phenomena.
The first part, organized into five chapters, focuses on vibrations. Chapter one introduces the
Lagrange formalism, which describes the oscillations of physical systems. Chapter two examines
free linear oscillations of systems with one degree of freedom under low amplitude conditions.
Chapter three addresses damped motion, incorporating the effects of viscous friction proportional to
velocity. The concept of resonance in forced oscillations is detailed in chapter four. Finally, chapter
five discusses vibrations in systems with multiple degrees of freedom, expanding the scope to more
complex scenarios.
The second part of the course, spanning the final two chapters, is dedicated to wave propagation
phenomena, offering a detailed treatment of the principles and applications of mechanical waves.
The course is presented in a logical and progressive manner, with each new concept supported by
simple examples and practical problems designed to reinforce understanding. This structure ensures
students can effectively assimilate the material, building a solid foundation in vibrations and
mechanical waves for applications in material science and technology.
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Keywords
Vibrations, Mechanical waves, Lagrange formalism, Resonance, Wave propagation.