Definition:Spring/Force Constant

Definition

Consider an ideal spring obeying Hooke's Law:

$\mathbf F = -k \mathbf x$

The constant of proportion:

$k \in \R_{>0}$

is known as the (spring) force contant.

Its value depends on the particular spring under investigation.

The SI unit of the force constant is newtons per metre: $\mathrm N \ \mathrm m^{-1}$.

Also known as

The force constant is also known as the stiffness of the spring.

The greater the value of $k$, the greater the stiffness.

Note, however, that the word stiffness can also be used to define how easy it is to bend something as opposed to stretching it (although the concepts are related).

So, to eliminate ambiguity, it is better to use the term (spring) force contant in the specific context of the "stretchiness" of a spring.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.20$: Vibrations in Mechanical Systems