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this video will show you the alternative way to derive the equation of motion for a multi degree of freedom system instead of using the conventional Newtons second law were using the Newtons law the directions of the force must be carefully analyzed and can be wrong if the analysis of the free body diagram is wrong lets begin deriving the equation of motion for m1 what you have to do is to put the reference point at m1 so the inertia force at m1 is straightforward m1 x1 double dot so here we have k1 attached to m1 and the deflections is x1 so the force is k1 X 1 for spring k2 it is compressed by x1 but extended by x2 because our reference is at m1 so this spring has total reflections of x1 minus x2 thus the force is K 2 multiplied by x1 minus x2 and this one is equals to 0 because we dont have any external exciting force now we have the first equation of motion for m1 you can now rearrange the equation to group the stiffness constants in X 1 and X 2 so we have m1 x1 double dot pl