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This video demonstrates an alternative method for deriving the equation of motion for a multi-degree-of-freedom system without using conventional Newton's second law. By carefully analyzing the directions of the forces in the system's free body diagram, errors in the analysis can be avoided. The equation of motion for m1 is derived by placing the reference point at m1 and considering the inertia force at m1 as m1 x1 double dot. The forces exerted by springs k1 and k2 on m1 are calculated based on the deflections x1 and x2. By setting the sum of the forces equal to 0, the first equation of motion for m1 is obtained, allowing for rearrangement to group the stiffness constants k1 and k2 with the variables x1 and x2.
