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Spring stretching under its own weight

Spring stretching under its own weight

Spring stretching under its own weight

(OP)
I remember solving this problem in calculus years and years ago, but am struggling with it now.  I’m working with a long, weak extension spring hanging vertically, and the spring constant is small enough that the spring stretches under its own weight.  How can I calculate the amount of stretch due to the spring’s weight at any given point along its length?

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