Question

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?

Answer 1

Explanation:

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

$k_{eff}=\dfrac{1}{\dfrac{1}{k_1}+\dfrac{1}{k_2}}$

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,

$\dfrac{1}{\dfrac{1}{k_1}+\dfrac{1}{k_2}}$

Hence, this is the required solution.