Two springs with constants k1 and k2 are in a series using the fact that force balance must apply everywhere, what is the equivalent spring constant of a single spring? that is, if you had to swap out a single spring for the two springs that are in series, what would its spring constant need to be to generate the same force at any displacement?

Explanation:

Let the spring constant of two springs are k₁ and k₂. In series combination of springs, the equivalent of springs is given by :

So, if it is required to swap out a single spring for the two springs that are in series, the spring constant need to be to generate the same force at any displacement is,

Hence, this is the required solution.

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