Hooke's Law Formula

F = k × x - The restoring force of a spring is proportional to its displacement from equilibrium. This holds within the elastic limit; beyond it the spring permanently deforms.

Spring constant reference

Spring type	Approximate k
Watch hairspring	~10 N/m
Bungee cord	~100 N/m
Stiff mattress spring	~500 N/m
Mechanical keyboard switch	~500–1,500 N/m
Car suspension spring	~15,000–40,000 N/m

Elastic potential energy

A compressed or stretched spring stores energy. The elastic potential energy is:

PE = ½kx²

For example, a spring with k = 500 N/m compressed by 0.1 m stores PE = ½ × 500 × 0.01 = 2.5 joules. This energy is released when the spring returns to equilibrium - the basis of mechanical watches, spring-loaded toys, and retractable pens.

Elastic limit

Hooke's Law only holds within the elastic region of a material. Beyond the elastic limit (the yield point), the material deforms plastically and will not return to its original shape when the force is removed. On a stress-strain curve, the elastic region is the initial linear portion; the yield point marks where the curve begins to bend.

Real-world applications

Shock absorbers: springs and dampers absorb road impacts in vehicles
Seismic isolators: large springs decouple buildings from ground motion
Mechanical keyboard switches: spring force determines actuation feel
Vehicle suspension: spring constant is tuned for ride comfort vs. handling
Medical devices: surgical retractors and stents use calibrated spring forces