Glossary

Hooke’s Law

Hooke’s law is a physical principle stating that the amount of force needed to extend a spring by a given distance scales linearly with respect to the distance.

That results in:

Fs = k⋅x

where:
Fs is the applied force in [N]
k is the spring constant in [N/mm]
x is the deformation in [mm]

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Relation to the elastic constants

Hooke’s law can be derived from the modulus of elasticity, E:

Hooke's Law formula illustrating the relationship between force, spring constant, and deformation in mechanics.
Hooke’s Law formula showcases the relationship between force, spring constant, and deformation in elastic materials.
Equation illustrating Hooke's Law: \( x = \Delta L \), representing spring deformation and its relationship with force.

Simple harmonic oscillation

The simplest mechanical oscillating system is a weight attached to a linear spring subject to only weight and tension. The system is in an equilibrium state when the spring is static. If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium. However, in moving the mass back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position, establishing a new restoring force in the opposite sense. If a constant force such as gravity is added to the system, the point of equilibrium is shifted. The time taken for an oscillation to occur is often referred to as the oscillatory period.

Animation of Hooke's law demonstrating a spring with a mass, illustrating force and deformation interplay.
Graph illustrating simple harmonic motion with axes labeled for displacement (amplitude) and time, highlighting the oscillation period.
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