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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.
A spring that obeys Hooke's Law with spring constant k will have a total system energy E of: [14] E = ( 1 2 ) k A 2 {\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}} Here, A is the amplitude of the wave-like motion that is produced by the oscillating behavior of the spring.
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
This relationship is known as Hooke's law. A geometry-dependent version of the idea [a] was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", [5] [6] a linear relationship commonly referred to as Hooke's law.
The linear elastic performance of a spring is parametrized by a constant of proportionality, called the spring constant. This constant is usually denoted as k (see also Hooke's Law ) and depends on the geometry, cross-sectional area, undeformed length and nature of the material from which the coil is fashioned.
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
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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.