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Lissajous Jules:     more detail

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1. Lissajous Lab
lissajous Lab lissajous Figures. lissajous (pronounced LEEsuh-zhoo) figureswere discovered by the French physicist jules Antoine lissajous.
http://www.math.com/students/wonders/lissajous/lissajous.html

Extractions: Lissajous Figures Lissajous (pronounced LEE-suh-zhoo ) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.

2. Lissajous Lab
lissajous Figures lissajous (pronounced LEEsuh-zhoo) figures werediscovered by the French physicist jules Antoine lissajous. He
http://www.mathcats.com/explore/lissajous/lissajous.html

Extractions: To operate: Click the Preset buttons at the left to see sample patterns. To make your own patterns, use the digital readouts at the right. Click near the top of a digit to increase its value; click near the bottom to decrease its value. Explanation of Readout Values xFreq the number of horizontal cycles for each frame of the plot. yFreq the number of vertical cycles for each frame of the plot. hueFreq This is the number of hue cycles for each frame of the plot. Each hue cycle represents a complete spectrum of colors. Samples This is the number of line segments which will be used to draw each frame of the plot. Increasing this number will make the curves appear smoother. Decreasing this number will exacerbate the aliasing in the plot (making it look more like string art than a mathematical curve). Lissajous (pronounced LEE-suh-zhoo ) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.

The Physics of the Harmonograph also by Andrew Purdam. The harmonograph waspioneered by the French physicist, jules Antoine lissajous in 1857.

Extractions: Encyclogram Mathematics Books Nature Agriculture Animals Biology ... A magic chalkboard leads you to interactive math activities: 3D geometry, tessellations, symmetry, polygons, conversions, number stories, multiplication, estimation, probability, using money, real-life problems, a math art gallery of geometric designs, MicroWorlds projects, and more.

4. Lissajous Curve -- From MathWorld
in 1815. They were studied in more detail (independently) by julesAntoinelissajous in 1857 (MacTutor Archive). lissajous curves
http://mathworld.wolfram.com/LissajousCurve.html

Extractions: They are sometimes known as Bowditch curves after Nathaniel Bowditch who studied them in 1815. They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857 ( MacTutor Archive ). Lissajous curves have applications in physics, astronomy, and other sciences. The curves close iff is rational Lissajous curves are a special case of the harmonograph with damping constants Special cases are summarized in the following table, and include the line circle ellipse , and section of a parabola parameters curve line a circle ellipse section of a parabola It follows that gives a parabola from the fact that this gives the parametric equations , which is simply a horizontally offset form of the parametric equation of the parabola Harmonograph Simple Harmonic Motion

5. Lissajous Lab
lissajous Figures. lissajous (pronounced LEEsuh-zhoo) figures werediscovered by the French physicist jules Antoine lissajous. He
http://www.control.co.kr/java4/lissajous.html

Extractions: Lissajous (pronounced LEE-suh-zhoo ) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.

6. Lissajous
(jules lissajous (18321880) was a French scientist who studied beams of lightreflected successively from two mirrors each mirror on a tuning fork).
http://astro.physics.sc.edu/S&ST/Lissajous/Lissajous.html

Extractions: To demonstrate how time may be represented as Distance, and the nature of Lissajous Figures Equipment - String, table salt (about half a cup full), styrofoam cup, sticky tape. sheet of contrasting (dark) paper. A picture of the trace was obtained (see figure) by replacing the dark paper by a transparent vinyl sheet as used in an overhead projector. The sheet can then be placed on the projector for all to see. or you can place it on a Xerox machine, cover the vinyl sheet with a sheet of dark paper, and copy it. The salt can be replaced by a felt tipped pen, but our experience is that it is very difficult to make this relatively friction less, and give a good trace. A simple device using a pen to display more complex Lissajous patterns employs a heavy platen, such as a book, or an 8.5 x I I inch sheet of card with a soft drink can taped underneath. This must have a very large inertia to counter the frictional forces provided by the pen. It is supported by its four corners from the comers of a small oblong of card or, better, a ruler as shown in the figure. The pen is taped to the end of two straws, as shown, which are pivoted using sticky tape, from the support (e.g. a book). The other end of the straws is counterbalanced so that the pen barely touches the paper. When set swinging, the device draws the most delightful pattern - however, these result from coupling between the torsional mode of the system, and the x and y modes. and are difficult to calculate. The length of strings, dimensions of book etc., make for many differences in pattern.

7. Lissajous Lab
lissajous Figures lissajous (pronounced LEEsuh-zhoo) figures werediscovered by the French physicist jules Antoine lissajous. He
http://www.crazybone.com/osc/osc.html

Extractions: Lissajous (pronounced LEE-suh-zhoo ) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.

8. Lissajous Figures
The optical production of the curves was first demonstrated in 1857 by jules AntoineLissajous (18331880), using apparatus similar to that at the left.
http://www2.kenyon.edu/depts/physics/EarlyApparatus/Oscillations_and_Waves/Lissa

Extractions: Lissajous Figures Lissajous Figures were first described in 1815 by Nathaniel Bowditch (1773-1838), who is best known today for his book, "The New American Practical Navigator", still available today. He also wrote widely on mathematics and astronomy, while pursuing a career as a navigator, surveyor, actuary and insurance company president, as well as being a member of the Corporation of Harvard College. The optical production of the curves was first demonstrated in 1857 by Jules Antoine Lissajous (1833-1880), using apparatus similar to that at the left. Today we can do the same experiment more easily with a laser beam that reflects from the two mirrors vibrating at right angles to each other and then traces the Lissajous figure on the wall. On the left is a pair of tuning forks permanently mounted at right angles to each other. The apparatus is shown in the 1900 catalogue of Max Kohl at a price of 66 Marks. It is in the collection at St. Mary's College in Notre Dame Indiana. The frequency of the tuning forks in both sets of apparatus can be varied by sliding masses up and down.

9. Lissajous Lab
Translate this page Figuras de lissajous Las figuras de lissajous (se pronuncia Li-su-sho)fueron descubiertas por el físico francés jules Antoine lissajous.
http://www.geocities.com/magotrix/lissajous/lissajous.htm

10. Lissajous
Translate this page Bowditch che le studio' nel 1815. Esse vennero studiate con piu' dettagli(indipendentemente) da jules-Antoine lissajous nel 1857.
http://www.geocities.com/Heartland/Plains/4142/lissajous.html

Extractions: Equazione cartesiana: x = a sin(nt+c), y = b sin(t) Le curve di Lissajous oppure figure di Lissajous sono talvolta chiamate curve Bowditch dal nome di Nathaniel Bowditch che le studio' nel 1815. Esse vennero studiate con piu' dettagli (indipendentemente) da Jules-Antoine Lissajous nel 1857. Le curve Lissajous hanno applicazioni in fisica, astronomia ed in altre scienze. Nathaniel Bowditch (1773-1838) era americano. Imparo' il latino per studiare i Principia di Newton e piu' tardi altre lingue per studiare la matematica in quelle lingue. Il suo New American Practical Navigator (1802) e la sua traduzione della di Laplace gli ottennero una reputazione internazionale. Altri siti Web University of Virginia, USA JOC/EFR/BS gennaio 1997

11. An Introduction To Lissajous Patterns
Background lissajous (pronounced LEEsuh-zhoo) figures were discoveredby the French physicist jules Antoine lissajous. He would
http://www.egr.msu.edu/classes/ece482/Teams/99spr/design2/web/resources/lissajou

Extractions: An Introduction to Lissajous Patterns First draft by Michael Kramarczyk,Chris Kolodz, Adam Matheny Updated by Michael Kramarczyk EE 482-Capstone: Computer System Design Michigan State University Property of: Design Team #2 : SPEED Draft: 4/23/99 Lissajous patterns created on the scope using 2 function generators Purpose Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.Lissajous figures are useful in the calibration of frequencies in tuning forks. With these properly calibrated tuning forks one is able to verify the functionality of police radar, or the tuning of musical instruments. A Lissajous pattern is a graph of one frequency plotted on the y axis combined with a second frequency plotted on the x axis. Y and X are both periodic functions of time t given by equations such as x = sin (w*n*t + c) and y = sin w*t. Different patterns may be

12. Lissajous
Translate this page jules Antoine lissajous. Né le 4 Mars 1822 à Versailles, FranceDécédé le 24 Juin 1880 à Plombières, France. lissajous entre
http://www.ac-nice.fr/physique/lissajous/biblio.html

Extractions: Lissajous s ' intéresse aux ondes et développe une méthode optique pour l'étude des vibrations . Au début , il étudie les ondes produites par un diapason à la surface de l'eau . In 1855 , il décrit une méthode d'étude des vibrations acoustiques par réflexion d'un rayon lumineux sur un écran , par un miroir lié à l'objet en vibration . Il obtient les courbes de Lissajous par réflexion successive de la lumière sur deux miroirs fixés sur deux diapasons vibrant à angle droit. Les courbes sont vues uniquement à cause de la persistence rétinienne. Lissajous étudia les mouvements observés quand les diapasons vibraient avec des fréquences différentes. Lissajous reçut le Prix Lacaze en 1873 pour ses travaux sur l'observation optique des vibrations. Retour à la page Courbes de Lissajous

13. Courbes De Lissajous
Translate this page Courbes de lissajous Courbes de lissajous Les courbes de lissajous ont étédécouvertes par le physicien francais jules Antoine lissajous .
http://www.ac-nice.fr/physique/lissajous/

Extractions: Avant l 'apparition des moyens de mesure électronique ( fréquencemètre , phasemètre...), les courbes de Lissajous ont été utilisées pour déterminer les fréquences des sons ou de signaux radio. Un signal de fréquence connue est appliqué à l' entrée de déviation horizontale d' un oscilloscope, et le signal dont on veut mesurer la fréquence est appliqué à l'entrée de déviation verticale. La figure résultante est une fonction du quotient des deux fréquences.

14. Tobias Preußer - Lissajous Figuren
Translate this page gleichzeitig in zwei aufeinander senkrecht stehenden Ebenen schwingen kann, beobachtetman lissajous-Figuren, die zuerst von jules Antoine lissajous 1857 in
http://cips02.physik.uni-bonn.de/~preusser/applets/lissajous/lissajous.html

15. Lissajous Curve
we can confine ourselves to the case a ³1. julesAntoine lissajous (1822-1880)discovered these elegant curves (in 1857) while doing his sound experiments.
http://www.2dcurves.com/higher/higherli.html

16. Courbe De Lissajous
Translate this page Autres nom figure de lissajous, courbe de Bowditch. Pour les intimes jouecourbe d'Alice. jules lissajous (1822-1880) physicien français.
http://www.mathcurve.com/courbes2d/lissajous/lissajous.shtml

17. Lissajous
jules Antoine lissajous (18221880) was a French physicist who was interested inwaves, and around 1855 developed a method for displaying them optically by
http://www.voicesync.org/lissajous.htm

Extractions: Download WinZip file Version Date release Jul, 14/2002 Size Try prototype of a 3d version Lissajous explorer . Enables visualization and interaction with Lissajous figures , a scattered composition of two waves, they represent a link between vibration and matter as composed grids are those found in crystalline substances. Includes preset values and a random generator, try the 115,187 preset pair an oscillating pattern of a butterfly wing. Hear the figure with the auto play feature, plays 3 octave midi chord with the selected M, N values in octave scale. Jules Antoine Lissajous (1822-1880) was a French physicist who was interested in waves, and around 1855 developed a method for displaying them optically by reflecting a light beam from a mirror attached to a vibrating object such as a tuning fork. Lissajous figures are also used in Cymatic research. Home

18. Lissajous
It was composed in 1978 in honor to the French physicist julesAntoine Lissajouswho built an instrument for measuring frequency based on the shape of
http://computerart.cic.unb.br/portfolios/visualmusic/tonaltimbres/prints/lissajo

Extractions: Lissajous next image [tonal timbres] Prints Click here to order a print! Sizes up to 100cm x 150cm (40"x 60"). Printed on textured fine art paper, matt finish. Ready for framing. Description The geometry defined by the timbre of a mathematical instrument based on the 4:5 just major Third interval. It was composed in 1978 in honor to the French physicist Jules-Antoine Lissajous who built an instrument for measuring frequency based on the shape of orthogonal vibration compositions. Keywords Musical intervals, orthogonal instrument, instrument inner geometry. Creation date September 23, 1995. Original Media Computer program. Location

19. Museum Information - Milton J. Rubenstein Museum Of Science & Technology
Understanding lissajous Figures lissajous (pronounced LEEsuh-zhoo) figureswere discovered by the French physicist jules Antoine lissajous.
http://www.most.org/cs_liss.cfm

Extractions: Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies. Lissajous figures often appeared as props in science fiction movies made during the 1950's. One of the best examples can be found in the opening sequence of The Outer Limits TV series. ("Do not attempt to adjust your picturewe are controlling the transmission.") The pattern of criss-cross lines is actually a Lissajous figure.

20. Figuras De Lissajous
Translate this page t + f y ). A trajetória da partícula não é mais uma elipse, mas sim uma linhadenominada de curva de lissajous, em honra de jules Antoine lissajous que foi
http://www.cefetba.br/fisica/NFL/fge2/lissajous.html

Extractions: Figuras de Lissajous Resnick (pg. 24). Esquematize a trajetória de uma partícula que se move no plano xy de acordo com as equações: x = x m cos( w t - p e y = 2x m cos( w t). . O diagrama mostrado na Fig. 41 é o resultado da combinação de dois movimentos harmônicos simples x = x m cos( w x t ) e y = y m cos( w y t + f y (a) Qual é o valor de x m / y m (b) Qual é o valor de w x w y (c) Qual é o valor de f y Os elétrons num osciloscópio são defletidos por dois campos de tal maneira que, em qualquer instante r, o deslocamento é dado por x = Acos( w t) e y = Acos( w t + f y ). Descreva a trajetória dos elétrons e determine sua equação quando

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