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Therefore, the spring constant k, and each element of the tensor κ, is measured in newtons per meter (N/m), or kilograms per second squared (kg/s 2). For continuous media, each element of the stress tensor σ is a force divided by an area; it is therefore measured in units of pressure, namely pascals (Pa, or N/m 2 , or kg/(m·s 2 ).
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being ...
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.)
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 ...
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 effective mass of the spring in a spring-mass system when using a heavy spring (non-ideal) of uniform linear density is of the mass of the spring and is independent of the direction of the spring-mass system (i.e., horizontal, vertical, and oblique systems all have the same effective mass). This is because external acceleration does not ...
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 ...
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.