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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.
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is = where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
An ideal constant-force spring is a spring for which the force it exerts over its range of motion is a constant, that is, it does not obey Hooke's law.In reality, "constant-force springs" do not provide a truly constant force and are constructed from materials that do obey Hooke's law.
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: T = 2 π m k {\displaystyle T=2\pi {\sqrt {\frac {m}{k}}}} shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small.
A prototypical elastic component is a coiled spring. 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 ...
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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.