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Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.
The frequency that appears in the generalised form of the characteristic equation (which is the same for this circuit as previously) + + ′ = is not the same frequency. In this case it is the natural, undamped resonant frequency: [20]
The previous equation can be written also as the following: = where =, in which represents the natural frequency, M and K are the real positive symmetric mass and stiffness matrices respectively.
These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.
Lines of constant damping ratio can be drawn radially from the origin and lines of constant natural frequency can be drawn as arccosine whose center points coincide with the origin. By selecting a point along the root locus that coincides with a desired damping ratio and natural frequency, a gain K can be calculated and implemented in the ...
For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties: mass and stiffness; (providing the system is undamped). The natural frequency, or fundamental frequency, ω 0, can be found using the following equation:
It can be seen that the constant , defined in the above equations has the dimensions of impedance (ratio of voltage to current) and is a function of primary constants of the line and operating frequency. It is called the “characteristic impedance” of the transmission line, and conventionally denoted by . [2] = + + = ( ) ( ) which holds ...
The natural frequency of the very simple mechanical system consisting of a weight suspended by a spring is: = where m is the mass and k is the spring constant.For a given mass, stiffening the system (increasing ) increases its natural frequency, which is a general characteristic of vibrating mechanical systems.