Functions Derivation Basic derivation theorems. Multivariable functions Introduction to differential equations. Particle and Rigid Bodies Kinematics. Particle and Rigid Bodies Dynamics.

By the end of this subject, students will be able to have: 1. knowledge and understanding of linear differential equations which are applicable in mechanical vibration problems 2. knowledge and understanding of key aspects of mechanical vibrations fundamentals; 3. the ability to apply their knowledge and understanding to identify, formulate and solve problems of mechanical vibrations using established methods; 4. the ability to combine theory and practice to solve problems of mechanical vibrations; 5. an understanding of applicable techniques and methods in mechanical vibrations, and of their limitations;

1.- Introduction to differential calculus 2.- Approach and resolution of systems of linear differential equations. 3.- Numerical methods of solving differential equations 4.- Single DOF systems: 4.1.- Undamped. Free vibrations 4.2.- Damped free vibrations. 4.3.- Forced vibrations. 4.4.- Transitory and permanent response. 4.5.- Resonance Concept. 5.- Two DOF systems: 5.2.- Undamped free vibrations. 5.3.- Damped free vibrations. 5.4.- Forced vibrations. 6.- Generalization to n DOF systems.

Master class Classroom exercises Laboratories exercices Personal work. Team Work