Eigen Modes and Frequencies

This lecture covers the concepts of eigen modes, natural frequencies, and the superposition principle in the context of standing waves on a vibrating string. The instructor demonstrates the search for eigen modes and frequencies through live simulations, emphasizing the stability of the numerical scheme and the separation of variables technique. The lecture explores the conditions for natural modes and frequencies, including fixed and free edges, and the determination of complex coefficients by initial and boundary conditions. The linear superposition of solutions is highlighted as a general solution to the wave equation, with a focus on the clean mode obtained through resonant excitation.