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This video demonstrates an alternative method to derive the equation of motion for a multi-degree-of-freedom system by using Newton's law. By carefully analyzing the directions of forces in the free body diagram, the correct equation can be obtained. Starting with m1, the inertia force is m1x1 double dot. The forces from springs k1 and k2 are calculated based on deflections x1 and x2. The equation is set equal to 0 as there are no external forces, resulting in the first equation of motion for m1. Stiffness constants are then grouped in terms of x1 and x2.