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Springs in series and parallel
Intermediate
Series reduces stiffness; parallel increases it.
k_p = k₁+k₂Springs in parallel share the displacement: k = k₁ + k₂ (stiffer). Springs in series share the force: 1/k = 1/k₁ + 1/k₂ (softer).
Two 100 N/m springs: parallel 200, series 50 N/m.
Series is the opposite of resistors in series for the same-looking formula; watch which quantity is shared.
In more detail
Springs in parallel have spring constants that add, while springs in series combine so that the reciprocal of the effective constant equals the sum of the reciprocals.
Real-world uses
- Car suspensions often combine springs in parallel to share loads.
- Series springs are used in precision force sensors.
- Engineers combine springs in parallel to make a stiffer suspension, and in series to create a softer one.
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Frequently asked questions
Why do parallel springs add?
Because each spring shares the same extension, so their forces add.
Why is the series constant smaller?
Because the same force stretches each spring, so the total extension is larger.
How do springs in series compare with a single spring?
The combined stiffness is smaller than either spring alone, because the total stretch is shared between them.
Related topics in Newton's Laws & Forces
Stokes' law · Terminal velocity of a sphere · Spring force · Hooke's law limits · Equilibrium of concurrent forces · Torque and equilibrium