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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.
where K is the spring constant and has the unit of N/m. The displacement x is measured from the undisturbed position of the spring (that is, X = 0 when F = 0 ). Substituting the two equations
A spring that obeys Hooke's Law with spring constant k will have a total system energy E of: [14] E = ( 1 2 ) k A 2 {\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}} Here, A is the amplitude of the wave-like motion that is produced by the oscillating behavior of the spring.
Energy per unit temperature change J/K L 2 M T −2 Θ −1: extensive Heat flux density: ϕ Q: Heat flow per unit time per unit surface area W/m 2: M T −3: Illuminance: E v: Wavelength-weighted luminous flux per unit surface area lux (lx = cd⋅sr/m 2) L −2 J: Impedance: Z: Resistance to an alternating current of a given frequency ...
The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
The spring is attached to the block and mounted to an immobile object on the other end allowing the block to be moved by the force of the spring =, where is the horizontal displacement of the block from when the spring is unstretched. On a horizontal surface, the normal force is constant and equal to the weight of the block by Newton's third ...
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.)
Usage of N⋅m is discouraged by the SI authority, since it can lead to confusion as to whether the quantity expressed in newton-metres is a torque measurement, or a measurement of work. [15] Another unit for work is the foot-pound, which comes from the English system of measurement. As the unit name suggests, it is the product of pounds for ...