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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
Springs, which represent the elastic component of a viscoelastic material, obey Hooke's law: = where σ is the applied stress, E is the Young's modulus of the material, and ε is the strain. The spring represents the elastic component of the model's response. [2]
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress. They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength .
The rate or spring constant of a spring is the change in the force it exerts, divided by the change in deflection of the spring. That is, it is the gradient of the force versus deflection curve. An extension or compression spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in.
Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler.
The slope of the initial, linear portion of this curve gives Young's modulus. Mathematically, Young's modulus E is calculated using the formula E=σ/ϵ, where σ is the stress and ϵ is the strain. Shear modulus (G) Initial structure: Start with a relaxed structure of the material. All atoms should be in a state of minimum energy with no ...
Note that ′ is constant, while ′ ′ is directly proportional to frequency (where time-scale is the constant of proportionality). Often, this constant τ {\displaystyle \tau } multiplied with angular frequency ω {\displaystyle \omega } is called the loss modulus η = ω τ {\displaystyle \eta =\omega \tau } .
x is the distance that the spring has been stretched or compressed away from the equilibrium position, which is the position where the spring would naturally come to rest [usually in meters], F is the restoring force exerted by the material [usually in newtons], and k is the force constant (or spring constant). This is the stiffness of the spring.