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Lissajous Figures
A Lissajous curve , also known as Lissajous figure or Bowditch curve , is the graph of a system of parametric equations : x=A\sin(at+\delta),\quad y=B\sin(bt), which describe the superposition of two perpendicular oscillations in x and y directions of different angular frequency (''a'' and ''b).'' The resulting family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail in 1857 by Jules Antoine Lissajous (for whom it has been named). Such motions may be considered as a particular of kind of complex harmonic motion. The appearance of the figure is sensitive to the ratio . For a ratio of 1, when the frequencies match a=b, the figure is an ellipse, with special cases including circles (, radians) and lines (). A small change to one of the frequencies will mean the x oscillation after one cycle will be slightly out of synchronization with the y motion and so the ellipse will fail to close and trace a curve slightly adjacent during the next orbit sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spirograph
Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965. The name has been a registered trademark of Hasbro Inc. since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched worldwide in 2013, with its original product configurations, by Kahootz Toys. History In 1827, Greek-born English architect and engineer Peter Hubert Desvignes developed and advertised a "Speiragraph", a device to create elaborate spiral drawings. A man named J. Jopling soon claimed to have previously invented similar methods. When working in Vienna between 1845 and 1848, Desvignes constructed a version of the machine that would help prevent banknote forgeries, as any of the nearly endless variations of roulette patterns that it could produce were ext ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Shift
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LTI System
In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response of the system to an arbitrary input can be found directly using convolution: where is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication, as is frequently employed by the symbol in computer languages). What's more, there are systematic methods for solving any such system (determining ), whereas systems not meeting both properties are generally more difficult (or impossible) to solve analytically. A good example of an LTI system is any electrical circuit consisting of resistors, capacitors, inductors and linear amplifiers. Linear time-invariant system theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Lissajous
Circular may refer to: * The shape of a circle * ''Circular'' (album), a 2006 album by Spanish singer Vega * Circular letter (other) ** Flyer (pamphlet), a form of advertisement * Circular reasoning, a type of logical fallacy * Circular reference * Government circular, a written statement of government policy See also * Circular DNA (other) * Circular Line (other) Circle Line or circular line is an expression commonly used to describe a circle route in a public transport network or system. Circle Line or Circular line may also refer to: Railways Asia Bangladesh * Chittagong Circular Railway China ... * Circularity (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mars Light
Mars Lights are signal-safety lights used in the United States and built by Mars Signal Light Company for railroad locomotives and firefighting apparatus. Mars Lights used a variety of means to cause the light to oscillate vertically, horizontally, or both, to catch the attention of motorists and pedestrians. Mars lights were developed by Jerry Kennelly, a Chicago firefighter who realized that oscillating lamps would benefit fire departments and railroads. He performed an operational test with the C&NW railroad in 1936, and Mars Lights began appearing on locomotives in the later 1930s. Tri Lite, Inc. announced their acquisition of the Mars Signal Light Company, effective January 23, 1991. Tri Lite still manufactures many of the traditional Mars Lights under the Tri Lite Mars brand. The company has updated the Mars "888" Traffic Breaker with energy-efficient light-emitting diodes replacing the earlier halogen incandescent bulbs. Design variations There were many models of Mars Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronics'', 2nd ed., , CRC Press, 2002, p. 62 In electronics, the term is usually applied to periodically varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds—variations of pressure in air or other media. In these cases, the waveform is an attribute that is independent of the frequency, amplitude, or phase shift of the signal. The term can also be used for non-periodic signals, like chirps and pulses. The waveform of an electrical signal can be visualized in an oscilloscope or any other device that can capture and plot its value at various times, with a suitable scales in the time and value axes. The electrocardiograph is a medical device to record the waveform of the ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Signature Analysis
{{unreferenced, date=February 2015 Analog signature analysis is electronic component and circuit board troubleshooting technique which applies a current-limited AC sinewave across two points of an electronic component or circuit. The resulting current/voltage waveform is shown on a signature display using vertical deflection for current and horizontal deflection for voltage. This unique analog signature represents the overall health of the part being analyzed. By comparing the signatures of known good circuit boards to those of suspect boards, faulty nets and components can be quickly identified. Analog Signature Analysis relies on a change in electrical characteristics to detect problems on a circuit board. Other terms * ATE diagnostics * Power off nodal impedance test * Power-off testing * Tracker signature analysis * VI testing * VI curves * Voltage-versus-current display * V/I trace test Typical equipment * Flying probe * Octopus * VI interceptor * V/I curve tracer * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscilloscope
An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetitive or single waveforms on the screen that would otherwise occur too briefly to be perceived by the human eye. The displayed waveform can then be analyzed for properties such as amplitude, frequency, rise time, time interval, distortion, and others. Originally, calculation of these values required manually measuring the waveform against the scales built into the screen of the instrument. Modern digital instruments may calculate and display these properties directly. Oscilloscopes are used in the sciences, medicine, engineering, automotive and the telecommunications industry. General-purpose instruments are used for maintenance of electronic equipment and laboratory work. Special-purpose oscilloscopes may be used to analyze an automotive ign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonograph
A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor. A simple, so-called "lateral" harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis, and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency and phase of the pendulums relative to one another, different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures. More complex harmonogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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