This lecture explores the concept of equilibrium in mechanics through two practical experiments involving beams and masses, demonstrating the balance between forces and the importance of constraints. The instructor illustrates the application of virtual work principles to determine the optimal equilibrium positions in the systems, emphasizing the significance of geometric constraints and the calculation of work done. Through mathematical derivations and geometric interpretations, the lecture delves into the complexity of finding equilibrium points and the interplay between forces and constraints in mechanical systems.