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A 2-dimensional spring system. In engineering and physics, a spring system or spring network is a model of physics described as a graph with a position at each vertex and a spring of given stiffness and length along each edge. This generalizes Hooke's law to higher dimensions.
Classic model used for deriving the equations of a mass spring damper model. 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.
Dependence of the system behavior on the value of the damping ratio ζ Phase portrait of damped oscillator, with increasing damping strength. Video clip demonstrating a damped harmonic oscillator consisting of a dynamics cart between two springs. An accelerometer on top of the cart shows the magnitude and direction of the acceleration.
As long as the system has no energy loss, the mass continues to oscillate. Thus simple harmonic motion is a type of periodic motion. If energy is lost in the system, then the mass exhibits damped oscillation. Note if the real space and phase space plot are not co-linear, the phase space motion becomes elliptical. The area enclosed depends on ...
In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system or allowed combination of values of the system's parameters, a point is ...
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.
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As an example, consider the 3-dimensional case: Define n = n 1 + n 2 + n 3. All states with the same n will have the same energy. For a given n, we choose a particular n 1. Then n 2 + n 3 = n − n 1. There are n − n 1 + 1 possible pairs {n 2, n 3}. n 2 can take on the values 0 to n − n 1, and for each n 2 the value of n 3 is fixed.