Generalized Conservative Oscillator: Particular Solutions and Modal Base

This lecture covers the resolution of the free conservative regime using specific solutions and the modal base in the context of a generalized conservative oscillator. Topics include the orthogonality of eigenvectors, normal coordinates, linear combination of solutions, and the reformulation of the free oscillator regime. The instructor explains the resolution by specific solutions, the characteristic equation, proper pulsations, and the writing of eigenmodes in index notations. Additionally, the lecture delves into the normalization of amplitudes, orthogonality of modal vectors, and the response to initial conditions, including the extraction of reference amplitudes and mode phases.