Springs in Series Behave Like Resistors in Parallel

The energy column is the interesting one

Half the constant times the travel squared gives 2.5 joules for one spring, 5 for the pair in series and 1.25 for the pair in parallel — under an identical 50 N load. The soft arrangement stores four times as much as the stiff one, because energy is force times distance and the soft one moves four times further. That is why a long soft spring makes a better shock absorber than a short stiff one of the same rating: absorbing a given impact means storing its energy somewhere, and the stiff spring runs out of travel before it has taken much in. It is also why a stiff assembly returns to position faster — it holds less to give back.

Cutting a spring in half doubles its constant

The series rule read backwards says so: a full-length spring is two half-length springs joined end to end, so each half must be twice as stiff as the whole. This is a genuinely useful workshop fact — a spring that is too soft can be shortened rather than replaced — and it also warns that a spring cut to fit is no longer the component on the datasheet. The rated maximum load is unchanged, but it is now reached at half the travel, and the energy the shortened spring can hold before bottoming out has halved. Coil springs are wound with the ends ground flat for a reason, so a cut end usually needs finishing before it will sit square.

Frequently asked questions

When does Hooke's law stop working?

When the spring is stretched far enough to deform permanently, and rather earlier than most people expect. Up to the elastic limit the force is genuinely proportional to the extension and the spring returns to its exact original length; past it, the metal yields and the spring comes back longer than it started, with a different constant from then on. A spring that no longer holds its rated load is usually one that was overextended once rather than one that wore out gradually. The linear model also fails at the other end, when the coils touch: the constant does not rise smoothly there, it goes effectively infinite.

Why is the constant a conductance and not a resistance?

Because of which quantity is shared and which one adds up. In a series circuit the current is common and the voltages add; in a series of springs the force is common and the displacements add. Force therefore lines up with current and displacement with voltage, which makes the spring constant — force per displacement — the counterpart of current per voltage, that is a conductance. Once the pairing is made the rest follows without any extra thinking: whatever combines reciprocally for conductance combines reciprocally for stiffness, in exactly the same arrangement.