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Why is spring force in a massless spring constant throughout the spring?

I had a similar question about tension is a massless string. This thread answered it for me. Tension on a massless string

Similarly, I want to prove that spring force in a massless spring is constant across throughout the spring. I thought it had to do with Newton's 2nd law too. If I consider a very small section of the spring, then forces at either ends of the spring should be equal in magnitude according to the 2nd law, because the section of the spring is massless. But what I don't understand is, a spring is coiled, unlike a string. So I am not sure if I can use the 2nd law here, because it's not a string. Is there another way I can prove this?

Qmechanic
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4d_
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    Whether the massless spring is coiled or not makes no difference. The same argument applies. You do not appear to be asking anything new here. – sammy gerbil Mar 07 '20 at 21:36
  • This question seems to be different from the quoted duplicate. The issue here is the spring constant, not the inertia of the medium. For example, I can imagine a massless spring having a spring constant that varies along its length (think two massless springs in series), but I can't imagine a massless string whose "mass" varies along the length. That being said, this comment might constitute an answer. – garyp Mar 08 '20 at 13:57

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Yes, You can extend the same argument as you used for the string. The shape and size, doesn't matter. However one should consider the shape and size while calculating torque.

Amsterdam6483
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