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Equation of motion of a massspring system 
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#1
Feb414, 12:09 PM

P: 151

hi, all. I am trying to derive the equation of motion of a mass spring system without using the
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? 


#2
Feb414, 02:52 PM

Sci Advisor
PF Gold
P: 1,325

$$ \ddot{x} = \frac{k x}{m} $$ ensures that the acceleration ##\ddot{x}## is negative when the displacement ##x## is postive. If you add a minus sign in front of ##m \ddot{x}##, you get a positive acceleration for a positive displacement. 


#3
Feb414, 02:54 PM

Sci Advisor
PF Gold
P: 1,325

I should also add that the base formula is ##F=ma##. Once you have figured out what ##F## is, the equation must be applied directly, without modifying the ##ma## part.



#4
Feb514, 04:38 AM

P: 151

Equation of motion of a massspring system



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