Spring reaction is proportional to deformation

Also called Hooke’s law, it is an empirical law which states that the force needed to extend or compress a spring by some distance is proportional with respect to the deformation of the spring.

Notes:

1. The spring is aligned in the positive direction of the \(x\)-axis, thus the deformation can be positive, in which case the spring is stretched, or negative, in which case the spring is compressed. The sign of the force indicates its direction along the \(x\)-axis.

Conditions:

1. \(x\) is small compared to the total possible deformation of the spring

2. Only applies to elastic deformations of the body, i.e. the body reverts to its initial state after the removal of force or load applied onto it.

Links:

1. Wikipedia, last formula in paragraph.

spring_reaction

Restoring force, or spring reaction, exerted by the spring due to the deformation.

Symbol:

F

Latex:

\(F\)

Dimension:

force

stiffness

stiffness of the spring.

Symbol:

k

Latex:

\(k\)

Dimension:

force/length

deformation

deformation of the spring.

Symbol:

Delta(l)

Latex:

\(\Delta l\)

Dimension:

length

law

F = -k * Delta(l)

Latex:

\[F = - k \Delta l\]