Discussion
When two springs are in series, the equivalent stiffness will be :
(Where K is spring stiffness)
Answer: C
The equivalent stiffness is \(\frac{K}{2}\).
Springs in series carry the same force, and their deflections add. So the reciprocals of the stiffnesses add:
\[ \begin{aligned} \frac{1}{K_{eq}} &= \frac{1}{K} + \frac{1}{K} = \frac{2}{K} \\ K_{eq} &= \frac{K}{2} \end{aligned} \]
Two equal springs end to end stretch twice as far under a given load, so the combination is half as stiff. 2K is the answer for two springs in parallel, where the stiffnesses add directly. K would mean the second spring adds nothing, and K/4 would be four springs in series.
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