The Spring Equation
In 1660, British physicist Robert Hooke discovered a fundamental law of classical mechanics: the amount of force required to stretch a spring is directly proportional to how far you are trying to stretch it.
If you pull a spring 1 inch, it fights back with 10 pounds of force. If you pull it 2 inches, it fights back with exactly 20 pounds of force. This perfectly linear relationship is called Hooke's Law.
The Spring Constant ($k$)
Every spring, rubber band, or piece of elastic metal in the world has a unique stiffness. This is represented by $k$, the Spring Constant, measured in Newtons per meter ($N/m$).
- A Low $k$ (like a slinky) means the spring is incredibly weak and stretches easily.
- A High $k$ (like the shock absorbers on a monster truck) means the spring is incredibly stiff and requires massive force to compress.
The Equation
Why is there a negative sign? Because Hooke's Law calculates the Restoring Force. If you pull the spring to the right (positive $x$), the spring fights back by violently pulling to the left (negative $F$).