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Here is a multiple spring and a block system. I need to find the maximum elongation of the spring.

enter image description here

I tried to take $mg-(k_1+k_2)x=0$, and find $x$ from there. The answer is coming wrong. It should be $2mg/(k_1+k_2)$. I know what I'm considering is wrong, as I'm finding $x$ at equilibrium position. But I don't know how to find $x_{max}$, which is needed here. Help will be appreciated.

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  • $\begingroup$ Hi and welcome to the Physics SE! Please note that we don't answer homework or worked example type questions. Please see this Meta post on asking homework/exercise questions and this Meta post for "check my work" problems. $\endgroup$
    – John Rennie
    Commented Aug 11, 2018 at 13:52
  • $\begingroup$ Not clear. Which spring? What is the starting position? A description of the problem is missing. $\endgroup$
    – sammy gerbil
    Commented Aug 12, 2018 at 9:41
  • $\begingroup$ @sammygerbil the block comes down (due to gravity), hence maximum elongation of $K_1$. $\endgroup$
    – Arka Seth
    Commented Aug 12, 2018 at 14:45
  • $\begingroup$ @sammygerbil consider K2 to be beside K1, in parallel. I guess we have to proceed similarly. $\endgroup$
    – Arka Seth
    Commented Aug 12, 2018 at 14:45

1 Answer 1

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It can be easily proved that motion of block is simple harmonic.Hence it follows that initial position is an extreme, and it’s measure from equilibrium position gives the amplitude. Obviously the block would reach other extreme position.Hence, the maximum elongation would be twice that of what you found.

Else, you can use conservation of mechanical energy of system of block and springs and get the same answer.

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  • $\begingroup$ I guess this problem is about the oscillating case, the block is moving up and down. As shown it looks to be static and the solution is the more simple mg−(k1+k2)x=0 ? $\endgroup$
    – PhysicsDave
    Commented Aug 11, 2018 at 14:04

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