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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.
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.)
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.
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.
The force in the spring is (roughly) the vertical force at the contact patch divided by the motion ratio, and the spring rate is the wheel rate divided by the motion ratio squared. I R = S p r i n g D i s p l a c e m e n t W h e e l D i s p l a c e m e n t . {\displaystyle IR={\frac {SpringDisplacement}{WheelDisplacement}}.}
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A spring system can be thought of as the simplest case of the finite element method for solving problems in statics. Assuming linear springs and small deformation (or restricting to one-dimensional motion) a spring system can be cast as a (possibly overdetermined) system of linear equations or equivalently as an energy minimization problem.