Hooke's law
Ut tensio, sic vis
— Robert Hooke, 1676
Hooke's law is Robert Hooke's observation that the amount of force you apply to a spring scales linearly with the distance it moves.
This means that the more force you apply to a spring, the further it moves, linearly — twice as much weight moves it twice the distance, and so on.
It also means the further you stretch a spring, the more force it uses to regain its original length — again, linearly. So if you stretch it a short distance, it moves back with little force, slowly; if you stretch it twice as far, it moves back with twice as much force, for twice as much speed, to regain its original length after the same amount of time has passed. That amount of time is dictated by the spring's length. (It then overshoots, but eventually settles down, essentially making a brief sine wave.)
Hooke's law was soon applied to the mechanical watch, including by Hooke himself, resulting in the invention of the hairspring.
Natural philosophy: Hooke's law
