Linear system with 1 dof
Damping: logarithmic decrement, energy dissipated in resonance conditions, structural damping
Writing the equations of motion by means of Lagrange's equations
Linearization of the equations of motion, determination of static equilibrium position, the stability of the static equilibrium

Systems with 2-n degree of freefom
Introduction to 2-degrees of freedom systems
Equations of Motion
Free Vibration Analysis of an Undamped system
Coordinate coupling and principal coordinates
Forced Vibration analysis
Semidefinite systems
Modelling a continuous systems as multidegree of freedom systems
Influence Coefficients
Potential and Kinetic energy expression in matrix form
Generalized coordinates and generalized forces, Using Lagrange's Equations to derive equation of motion, equation of motion in matrix form
Eigenvalue Problem
Vibrating system with rigid motion, free response, forced response
solution of the dynamic problem in principal coordinates, Forced response in the principal coordinates, free response in principal coordinates
Control of Vibration, Control of Natural frequencies, introduction to dumping, Vibration Isolation, Vibration Absorber

Rotating shafts
Whirling of Rotating Shaft, rigid support and stiff shaft, stiff support and rigid shaft
Dynamic and static Balancing of Rotating Machine

Continuous Systems
Continuous systems, transverse vibrations of cables, transverse and axial vibrations of beams, torsional vibration of shafts, the boundary conditions for the determination of the equation of frequencies, remarkable cases

Finite Elements
Equations of Motion of an Element
Beam Element: Mass Matrix, Stiffness Matrix
Transformation of Element Matrices and Vectors
Equation of motion of the complete system, Boundary Conditions, consistent and Lumped-mass matrices