Math Playground
Physics

Spring

Hooke's law: F = −kx. Push or pull — the spring pushes back proportionally.

A spring obeys Hooke's law — force is proportional to stretch.

Try this
0.1
F = −k·x (k = 200 N/m; magnitude shown) = 20
Spring — pull the block, let it bounce (Hooke's law)
x = 0F = −kxtime →

stiffer spring or lighter mass ⇒ faster bounce: ω = √(k/m) = 3.46 rad/s, period T = 2π√(m/k) = 1.81 s. The red arrow is the restoring force F = −kx — always pointing back toward x = 0.

Hooke's law & elastic PE

The minus sign means the force always points back toward the rest position. Energy stored grows with the *square* of the stretch.

Your turn

A spring with k = 300 N/m is stretched 0.20 m. How much elastic potential energy is stored?

Watch out

Hooke's law only holds up to the elastic limit. Stretch a spring too far and it deforms permanently — F = −kx no longer applies.

Hooke's law
Elastic PE