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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.
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.)
In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]
Jun-ichi Ueda and Yoshiro Sadamoto have found [1] that as increases beyond , the effective mass of a spring in a vertical spring-mass system becomes smaller than Rayleigh's value and eventually reaches negative values at about . This unexpected behavior of the effective mass can be explained in terms of the elastic after-effect (which is the ...
When > and > the spring is called a hardening spring. Conversely, for β < 0 {\displaystyle \beta <0} it is a softening spring (still with α > 0 {\displaystyle \alpha >0} ). Consequently, the adjectives hardening and softening are used with respect to the Duffing equation in general, dependent on the values of β {\displaystyle \beta } (and α ...
A mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system tends to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate. The damping ratio ...
That followed a downwardly revised 1.1% pace of decline in the second quarter. Labor costs were previously reported to have advanced at a 2.4% rate in the April-June quarter.
The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modelling object with complex material properties such as nonlinearity and viscoelasticity. Packages such as MATLAB may be used to run simulations of such models. [1]