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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.
Equivalent Spring Constant (Series) When putting two springs in their equilibrium positions in series attached at the end to a block and then displacing it from that equilibrium, each of the springs will experience corresponding displacements x 1 and x 2 for a total displacement of x 1 + x 2. We will be looking for an equation for the force on ...
Flexibility is the inverse of stiffness. For example, consider a spring that has Q and q as, respectively, its force and deformation: The spring stiffness relation is Q = k q where k is the spring stiffness. Its flexibility relation is q = f Q, where f is the spring flexibility. Hence, f = 1/k.
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.
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.
A linear constant coefficient system is stiff if all of its eigenvalues have negative real part and the stiffness ratio is large. Stiffness occurs when stability requirements, rather than those of accuracy, constrain the step length. Stiffness occurs when some components of the solution decay much more rapidly than others. [3]
Stiffness is the extent to which an object resists deformation in response to an applied force. [ 1 ] The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Hooke's law gives the relationship of the force exerted by the spring when the spring is compressed or stretched a certain length: = (), where F is the force, k is the spring constant, and x is the displacement of the mass with respect to the equilibrium position. The minus sign in the equation indicates that the force exerted by the spring ...