Lecturer: M. Fabbrichesi , SISSA

In this lesson the professor continues with the problem of small oscillations but this time in n dimensions. This problem reduces to an **eigenvalues and eigenvectors** problem. In this lesson are introduced the **normal coordinates** and **normal mode** definitions. The professor solve two examples a mathematical example of two dimension and the free vibration of a linear triatomic molecule, composed by two atoms of mass *m* symmetrically located on each side of an atom of mass *M* and connected by a spring of constant *k*. He considers the case where the system makes small oscillations along the line of the molecule. In this lesson the professor give three more problems for the homework number 3 (Homework.3.2).

In this lesson on Classical Mechanics given in the MIT University the professor focused in the forced oscillations, normal modes, resonance natural frequencies and musical instruments. During the lesson instructive experiments are made to illustrate the theory, enjoy.

Normal Modes ExperimentAn experiment made by students with a PMMA square plate (30 x 30 cm), fixed to a 30 Watt speaker. The induced frequencies run from 0 to 500 Hz and they found modes at the following ones: 65 Hz, 80 Hz, 180 Hz, 340 Hz, 500 Hz with beautiful patterns.