# Definition:Spring/Ideal

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## 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

- $k \in \R_{>0}$

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