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This lecture covers the resolution of forces and energy calculations in mechanics, focusing on the application of Newton's laws and trigonometric formulas to determine the equilibrium and motion of objects. The instructor explains the concepts of force, work, and energy, providing step-by-step examples to illustrate the calculations involved in determining the equilibrium of systems. Additionally, the lecture delves into the calculation of potential and kinetic energy, emphasizing the importance of understanding these concepts in the context of mechanical systems.