Second year

The Physics 3 module (Mechanical Vibrations) studies oscillatory motions that represent the periodic back-and-forth movements of mechanical systems around an equilibrium point. It covers the analysis of free (without external force) and forced (with excitation) oscillators in the case of linear systems with one or more degrees of freedom whose behavior is governed by the linear Lagrange differential equations. Damping systems are structures or devices designed to reduce vibrations by dissipating energy, often through the use of passive materials or components. These dampers improve stability, comfort, and safety, particularly in buildings, vehicles, and mechanical equipment. Their effectiveness depends on parameters such as stiffness and the damping coefficient, which influence the system's dynamic response. In mathematical models, the total solution of the resulting differential equation includes a homogeneous part and a particular solution, reflecting the interaction between external forces and internal dissipation. The vibrating systems are characterized by their natural modes, determined by the initial conditions and the system's structure. External excitation F(t) introduces energy, leading to dynamic responses that can result in phenomena such as resonance. Understanding these concepts is essential for structural analysis in engineering and applied physics.

The Physics 4 module (Physics of Waves) focuses on the study of wave phenomena, which are ubiquitous in physics. A wave is a temporary disturbance that carries energy in a given direction without any overall displacement of matter. A wave can be longitudinal if the transient oscillation occurs in the direction of the wave and induces a deformation parallel to the direction of propagation, while it becomes transverse when it generates a deformation perpendicular to the direction of propagation. Wave phenomena are classified into two distinct categories according to their physical nature. The first category consists of mechanical waves generated by small disturbances in a material medium, such as waves on vibrating strings, acoustic waves in fluids and solids, seismic waves, and ultrasonic waves in biology and medicine. As for the second category, it does not correspond to disturbances in a material system; therefore, it does not require a material medium to propagate. Examples include electromagnetic waves linked to the combined local variations of electric and magnetic fields. These waves can propagate perfectly well in a vacuum, but also in material media, provided the latter are sufficiently transparent. When these waves are perceptible to the eye, i.e., in the visible wavelength range, they are usually called light waves. This is one of the main areas of application for wave physics. These wave phenomena are described by D'Alembert's equation, a second-order partial differential equation that describes the propagation of waves (mechanical, sound, and light) at a well-defined speed C. This equation is essential in mechanics, electromagnetism, and acoustics, since it allows the modeling of wave phenomena at constant speed. Its general integral, given by d'Alembert's formula, illustrates the superposition of two waves propagating in opposite directions.

The Physics 3: Vibrations and Waves module introduces students to the fundamental principles governing oscillatory motion and wave phenomena in mechanical and physical systems. The course begins with the study of simple harmonic motion, exploring the dynamics of oscillators, energy exchange, damping mechanisms, and forced vibrations. Students learn how resonance arises and how it influences real physical systems.

The module then extends these concepts to wave propagation, focusing on the description of mechanical waves in strings, air, and other media. Key topics include wave equations, characteristics of traveling and standing waves, impedance, reflection and transmission at boundaries, and energy transport. Practical applications such as sound waves, vibrating strings, and acoustic phenomena are emphasized through demonstrations and laboratory work.

By the end of the course, students gain a solid understanding of how vibrations and waves behave, how they interact with matter, and how these principles underpin many technologies in physics and engineering.