Definition:Spring/Ideal

Definition

An ideal spring obeys Hooke's Law:

$\mathbf F = -k \mathbf x$

where:

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

Sources

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