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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 second law, it is crucial to carefully analyze the directions of force to avoid inaccuracies in the free body diagram. To begin deriving the equation for m1, place the reference point at m1 to determine the inertia force as m1 x1 double dot. With k1 and k2 springs attached to m1, the forces are k1 x1 and k2(x1 - x2) respectively. By setting the sum of forces to 0, the equation for m1 can be rearranged to group stiffness constants in x1 and x2.