Harmonic Oscillations: Equilibrium and Stability

This lecture focuses on harmonic oscillations, specifically discussing equilibrium points, stability analysis, and the concept of natural frequency. The instructor explains the behavior of systems with mass and springs, emphasizing the importance of small angle approximations. The lecture covers the derivation of equations of motion for different systems, such as a mass attached to a spring. Through examples and demonstrations, the instructor illustrates how to determine stable and unstable equilibrium points. The lecture concludes with a discussion on the general applicability of harmonic oscillation models in various physical systems, highlighting the fundamental properties of oscillatory motion.