Conservation of Mechanical Energy: Systems with Conservative Forces

This lecture covers the concept of conservation of mechanical energy in systems where all forces are conservative. It demonstrates how the mechanical energy remains constant in such systems and explores the evolution of a system with conservative forces between different states. The lecture also discusses equilibrium points, stability, and the behavior of systems near stable equilibrium points. Examples such as a mathematical pendulum and a bungee jump are used to illustrate the application of the conservation of mechanical energy. The presentation includes detailed explanations and mathematical derivations to provide a comprehensive understanding of the topic.