Conservation of Mechanical Energy

This lecture covers the conservation of mechanical energy in systems with conservative forces, demonstrating that if all forces are conservative, mechanical energy remains constant. It explores the relationship between kinetic and potential energy, as well as the impact of non-conservative forces on energy. The lecture delves into the stability of equilibrium points in systems, analyzing the behavior of systems with one degree of freedom. Examples such as the mathematical pendulum and bungee jumping are used to illustrate the concepts. The lecture concludes with a discussion on phase portraits and the visualization of trajectories in phase space.