I Spring within a spring

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1. Nov 30, 2016

Laxbro112

So I am doing tensile testing on an elastic electrical lead for biomedical purposes. The lead is encapsulated in an elastic tubing. Now the lead acts like a weak spring itself (coiled wire).
I'm curious, if there are two springs with different k constants "within" each-other (one inside the other) will it effect the Hooke's law equation? Or will the dominant k constant be the baseline?

2. Nov 30, 2016

RUber

If you have two springs with the same k embedded into each other, what would happen? I think since the density of the spring is changed, you would have a greater stiffness. Would you use 2k and just add the two? If the springs were separate and working together you could assume that they work together.

Using
$F = k_1X_1 + k_2X_2$,
you can see that if the displacement is the same, the effective k is the sum of the two.

If the second is much weaker than the first, ignoring it will likely not induce a significant error.