Hookella

Meet Hookella, a spring who always pulls back toward where she started.

In 1676 Robert Hooke published an anagram, and in 1678 its answer, ut tensio, sic vis: as the extension, so the force. Stretch or compress an ideal spring by a distance x and it pushes back with a force proportional to x. The constant k measures stiffness, and the minus sign says the force points opposite to the displacement.

Example: a spring with k = 200 N/m stretched by 5 cm pulls back with 200 × 0.05 = 10 newtons. The energy stored is ½kx², here 0.25 joules.

A mass on a Hooke's-law spring oscillates in simple harmonic motion, and the same law describes small vibrations of almost anything: atoms in solids, bridges and buildings. Spring scales and car suspensions rely on it.

Real springs follow the law only up to their elastic limit. Beyond it, they deform permanently or break, and many materials, like rubber, are never quite linear.