Hooke's Law
#Physics
$\displaystyle \vec{F}_{\text{spring}}=-k\vec{x}$
- $\displaystyle \vec{F}_{\text{spring}}$ is the elastic force provided by a spring or elastic component on the object the spring is attached to
- $\displaystyle k$ is the spring constant of the spring
- $\displaystyle \vec{x}$ is the displacement of the object from its equilibrium position
$\displaystyle \vec{F}{ij}=-k{ij}\Delta \vec{r}_{ij}$
- $\displaystyle \vec{F_{ij}}$ is the spring force between two points
- $\displaystyle k_{ij}$ is the spring constant between the points
- $\displaystyle \Delta \vec{r}_{ij}$ is the deformation between two points from equilibrium
$\displaystyle k_{ij}=E \frac{A_{ij}}{L_{0ij}}$
- $\displaystyle E$ is Young's modulus
$$
\begin{align}
\vec{F}{ij}&=-k{ij}\Delta \vec{r}{ij} \\\sigma{ij}&=E\varepsilon_{ij}
\end{align}
$$
$\displaystyle \vec{F}{ij}=-k{ij}\Delta \vec{r}_{ij}$
$\displaystyle \vec{F_{ij}}$ is the spring force between points $\displaystyle i,j$
- $\displaystyle k_{ij}=E \frac{A_{ij}}{r_{0ij}}$ is the spring constant between $\displaystyle i,j$
- $\displaystyle A_{ij}$ is the area between $\displaystyle i,j$
- $\displaystyle r_{0ij}$ is the equilibrium distance between $\displaystyle i,j$
- $\displaystyle \Delta \vec{r}_{ij}$ is the deformation between $\displaystyle i,j$ from equilibrium
$\displaystyle \sigma_{ij}=E\varepsilon_{ij}$
- $\displaystyle \sigma_{ij}$ is the stress between points $\displaystyle i,j$
- $\displaystyle E$ is the Young's modulus of the material
- $\displaystyle \varepsilon_{ij}=\frac{\Delta r_{ij}}{r_{0ij}}$ is the strain between $\displaystyle i,j$