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It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
The Titius–Bode law was regarded as interesting, but of no great importance until the discovery of Uranus in 1781, which happens to fit into the series nearly exactly. Based on this discovery, Bode urged his contemporaries to search for a fifth planet. Ceres, the largest object in the asteroid belt, was found at Bode's predicted position in 1801.
A Bode plot of displacements in the system with (red) and without (blue) the 10% tuned mass. The Bode plot is more complex, showing the phase and magnitude of the motion of each mass, for the two cases, relative to F 1. In the plots at right, the black line shows the baseline response (m 2 = 0).
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
The Bode plot of a first-order low-pass filter. The frequency response of the Butterworth filter is maximally flat (i.e., has no ripples) in the passband and rolls off towards zero in the stopband. [2] When viewed on a logarithmic Bode plot, the response slopes off linearly towards negative
Numerous tools exist for the analysis of the poles of a system. These include graphical systems like the root locus, Bode plots or the Nyquist plots. Mechanical changes can make equipment (and control systems) more stable. Sailors add ballast to improve the stability of ships.
The number of parameters in the Duffing equation can be reduced by two through scaling (in accord with the Buckingham π theorem), e.g. the excursion and time can be scaled as: [2] = and = /, assuming is positive (other scalings are possible for different ranges of the parameters, or for different emphasis in the problem studied).