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Springs in series and parallel

When several springs carry the same mass, they can be replaced by one equivalent spring. In parallel they share the displacement equally, and the stiffnesses add. In series they share the force equally, and it is the flexibilities (1/k) that add, just like for electrical resistors.

kpar=k1+k2k_{par} = k_1 + k_2springs in parallel
kser=k1k2k1+k2k_{ser} = \dfrac{k_1k_2}{k_1+k_2}springs in series

Symbols

kpar, kserk_{par},\ k_{ser}equivalent stiffnessN/m
k1, k2k_1,\ k_2individual spring stiffnessN/m

Example

Two springs of 200 N/m and 300 N/m in series:

kser=200⋅300/500=120k_{ser} = 200\cdot 300/500 = 120 N/m.

In series the equivalent stiffness is always less than the weakest spring alone.
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