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An ideal spring obeys Hooke's Law:

$\mathbf F = -k \mathbf x$


$\mathbf F$ is the force caused by a displacement $\mathbf x$
$k$ is the constant of proportion.

The negative sign indicates that the force pulls in the opposite direction to that of the displacement imposed.

Spring Force Constant

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: $\mathrm N \ \mathrm m^{-1}$.