Springel

Meet Springel, two springs joined end to end who share the load but stretch twice as far.

When springs hang in series, the same force passes through each one. Each spring stretches by its own amount, and the total stretch is the sum. That makes the pair softer than either spring alone.

The combined stiffness follows 1/k = 1/k₁ + 1/k₂. Two springs of 100 N/m each give k = 50 N/m. Hang a 1.0 kg mass and its weight of 9.81 N stretches the pair by about 0.20 m, compared with about 0.10 m for one spring.

Springs side by side in parallel work the opposite way. Their stiffnesses simply add, so two of them together are twice as stiff.

Curiously, the rule for springs in series looks just like the rule for resistors in parallel. Car suspensions and mattresses combine springs in both ways to get the feel designers want. The same reasoning gives the stiffness of many springs side by side: just add them up.