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about the way it stretches - the beginning is stretched the most, since it is being stretched by the whole cord below, as it goes down it is stretched less and less until at the end it is essentially not streched at all.

And so I started wondering, how could one find it's density distribution, assuming it is not a curled spring, but say, a rubber band, heavy enough to be streched by gravity of it's own weight, but not as much so that Hooke's law would be innapplicable.

Now when I try writting equations, I get into trouble. I assumed, that each infinitessimal lengh interval could be increased by some extra ammount due to stretching of the spring below it, but according to Hooke's law, that is a finite amount, which is proportional to the mass below. Thus if I integrate that, I'll get an infinity. Either way I attack the problem, I get a missmatch of infinitesimal vs. finite quantities.

So the question is, how should I attack this problem and get consistent equations ? Are any of my assumptions wrong (Hooke's law e.g.) ?