胡克定律：使应力和应变有联系

Hooke's law states that the force exerted by a spring is: $$F=-kx$$ where k is a constant (units: $N/m$), and $x$ is the distance the spring is stretched from its natural position (where it is when no forces are acting on it).

There a a few natural outcomes of this. First, by integrating force over distance, we get the potential energy of the spring: $$E=\frac{1}{2}kx^2$$ Second, if we have a constant force acting on the spring, it is the equivalent of changing $x$. $$F=-kx+N=-k(x-\frac{N}{k})$$ As we see in the previous equation, this is equivalent to changing the natural position of the spring by $\dfrac{F}{k}$, where $F$ is the constant force.