hi, all. I am trying to derive the equation of motion of a mass spring system without using the(adsbygoogle = window.adsbygoogle || []).push({});

energy method but I am wrong somewhere and I cant find it, can you help me find where I am

wrong. Equation of motion of a simple mass spring system is indeed mx''+kx=0 but here I am

thinking that when we pull the mass, motion arises from the spring force which is trying to bring back the mass and it is -kx due to our choice of negative direction but when the force is negative,

i.e -kx, the acceleration x'' must also be negative because they are in the same direction and sense. Here their sense both are negative. So equation should be -mx''=-kx(sum of forces equal mass product acceleration) and thus -mx''+kx=0 Can you explain me where I am wrong?

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# Equation of motion of a mass-spring system

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