Harmonic Oscillator II: Damped, Forced, Beats, Resonance

This lecture covers the stability condition in a system, forces of constraint, homogeneous and particular solutions, and the new chapter on a forced oscillator. The instructor explains the interaction between the natural frequency and the forcing frequency, the concept of resonance, and the effects of damping on the system. The lecture also delves into the phenomenon of beats, where the amplitude of the output is dependent on the excitation frequency, and demonstrates resonance through various experiments involving pendulums and sound waves. The mathematical analysis includes solving differential equations for the damped and forced harmonic oscillator, exploring the behavior of the system under different conditions, and understanding the complex interplay between damping, forcing, and resonance.