Potential Energy, Mechanical Energy, and Resonance

This lecture covers topics such as equilibrium, stability, potential energy, mechanical energy, and resonance. It discusses the concept of stable and unstable equilibrium, the potential energy function, conservative forces, and the stability criteria. The lecture also explores the behavior of forced harmonic oscillators, transient and steady-state regimes, and harmonic response. Practical examples of resonance phenomena, such as acoustic resonance in trombones and diapasons, are presented. The instructor illustrates the effects of resonance through experiments involving metronomes, glass shattering due to acoustic resonance, and the collapse of the Tacoma Narrows Bridge. The lecture concludes with a discussion on the synchronization of metronomes and the phenomenon of 'Bianca Castafiore'.