21. 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

Home Teacher Parents Glossary ... Email this page to a friend More Wonders Fractals Spirograph Conway's Game of Life Roman Numeral Calculator ... Lissajous Lab Resources Cool Tools References Test Preparation Study Tips ... Wonders of Math Search Lissajous Lab 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. 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

22. 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

contents Lissajous Lab 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 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.

23. Kosmoi: Encyclogram: Links The Physics of the Harmonograph also by Andrew Purdam. The harmonograph waspioneered by the French physicist, jules Antoine lissajous in 1857. http://kosmoi.com/Science/Mathematics/Graphs/Encyclo/links.shtml

Encyclogram Mathematics Books Encyclogram: Links Nature Agriculture Animals Biology ... Harmonograph The two pendulum harmonograph draws attractive patterns that arise from drawing the relative path traversed by two swinging masses as their motion is slowly damped. The resulting figures are called harmonograms or sometimes a Lissajous curve. Harmonograph from MathWorld A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, complicated curves which eventually terminate in a point as the motion of the pendula is damped by friction. In the absence of friction (and for small displacements so that the general pendulum equations of motion become simple harmonic motion), the figures produced by a harmonograph would be Lissajous curves. Emulation of Questacon's Harmonograph Java applet by Andrew Purdam. Well worth a look! The Physics of the Harmonograph also by Andrew Purdam. "The harmonograph was pioneered by the French physicist, Jules Antoine Lissajous in 1857. The first harmonograph actually used a light beam on a screen (funny how history repeats itself!) Following the invention of the harmonograph it became a very popular device and was found in many homes. After the early 1900s it decreased in popularity and is rarely seen today, except in hands-on science centres." mathcats 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.

24. 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

Geometry Curves Plane Curves General Plane Curves Lissajous Curve Lissajous curves are the family of curves described by the parametric equations sometimes also written in the form 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 References Cundy, H. and Rollett, A. "Lissajous's Figures." §5.5.3 in Mathematical Models, 3rd ed.

25. 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

Lissajous Lab To operate: Select the Preset buttons at the left to see sample patterns. To generate your own patterns, use the digital readouts at the right. Adjust the readouts by clicking on the digits: clicking near the top of a digit increases its value; clicking near the bottom decreases its value. 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. 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

26. 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

LISSAJOUS FIGURES 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.

27. 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

Lissajous Lab To operate: Select the Preset buttons at the left to see sample patterns. To generate your own patterns, use the digital readouts at the right. Adjust the readouts by clicking on the digits: clicking near the top of a digit increases its value; clicking near the bottom decreases its value. 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. 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

28. 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

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.

29. 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

Figuras de Lissajous Instrucciones: Selecciona uno de los botones con letras de lado izquierdo para ver figuras precalculadas. Para generar tus propias figuras, usa los números de la derecha. Haciendo click en la parte superior de un dígito se incrementa su valor Haciendo click en la parte inferior de un dígito se decrementa su valor. Explicación de los valores de las lecturas xFreq Es el número de ciclos horizontales por cada cuadro del dibujo. yFreq Es el número de ciclos verticales por cada cuadro del dibujo. hueFreq Es el número de ciclos del color por cada cuadro de la figura. Cada ciclo representa un espectro completo de colores. Samples Es el número de segmentos de línea que se usarán para dibujar cada cuadro. Incrementar este número hace las curvas más suaves. Decrementarlo, aumenta la inclinación de cada línea, haciéndolo parecer más macramé que una curva matemática. Figuras de Lissajous Las figuras de Lissajous (se pronuncia Li-su-sho ) fueron descubiertas por el físico francés Jules Antoine Lissajous . Él usó sonidos de diferentes frecuencias (agudos y graves) para hacer vibrar un espejo. Un rayo de luz reflejado en el espejo dibujaba figuras, cuya forma dependía de la frecuencia de los sonidos. El experimento de Lissajous es similar al aparato que se utiliza en la actualidad para proyectar espectáculos de luz lasser.

30. 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

Curve di Lissajous 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 Traduzione di Mike Notte Siete pregati di notificare Mike Notte di qualsiasi improprieta' di lingua italiana. Grazie. Per la bibliografia, per esaminare le Curve Associate, e per operare interattivamente sulla curva usando Java, andare al testo originale: www-groups.dcs.st-and.ac.uk/~history/

31. 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

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 This application note describes the functionality of Lissajous patterns and how they are used to calibrate the frequency of waveform. Background 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

32. 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

Jules Antoine Lissajous Né le : 4 Mars 1822 à Versailles, France Lissajous En 1850 il obtient son doctorat pour une thèse sur l'enregistrement des vibrations 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

33. 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/

Courbes de Lissajous Courbes de Lissajous Les courbes de Lissajous ont été découvertes par le physicien francais Jules Antoine Lissajous 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. Vous disposez d' un oscilloscope virtuel avec lequel vous pourrez générer différentes figures . Vous pouvez faire varier la fréquence horizontale xFREQ. Vous pouvez également faire varier la fréquence verticale yFREQ .) L' application JAVA permet aussi d' appliquer un signal hueFREQ pour moduler la nuance de la trace, on peut ainsi créer des figures colorées.. Comment opérer: Pour obtenir vos propres courbes , utiliser les compteurs digitaux à droite. Ajuster les compteurs en cliquant sur les chiffres: en cliquant près du haut du chiffre vous augmentez sa valeur ; en cliquant près du bas vous la diminuez .

34. 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

Lissajous Figuren Bei einem System, das gleichzeitig in zwei aufeinander senkrecht stehenden Ebenen schwingen kann, beobachtet man Lissajous-Figuren, die zuerst von Jules Antoine Lissajous 1857 in Paris demonstriert wurden: Ihr Browser kann leider keine Java-Applets anzeigen. Schade. f (t) = A sin (w t) f (t) = A sin (w t + p) Im Fall der oben zu sehenden Figuren ist die Frequenz w ganzzahliges Vielfaches der Frequenz w erfolgt alle paar Minuten neu. Die beiden maximalen Amplituden sind im Applet immer gleich. Die Phase p Suchen Sie sich einen Punkt der Figur. Wenn die erste Schwingung nun die Amplitude hat, die Sie in diesem Punkt auf der X-Achse ablesen, dann hat die zweite Schwingung die Amplitude, die Sie in diesem Punkt auf der Y-Achse ablesen. p p Document changed last on (preusser@cips02.physik.uni-bonn.de) 1996 Access statistics by Nedstat

35. 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

Lissajous curve higher last updated: where b £ p When the constant a is rational, the curve is algebraic and closed. If a is irrational, the curve fills the area [-1,1] x [-1,1]. It is easy to see that the curves for 1/a and a are equal in form. This means that we can confine ourselves to the case a Jules-Antoine Lissajous (1822-1880) discovered these elegant curves (in 1857) while doing his sound experiments. But it is said that the American Nathaniel Bowditch (1773-1838) found the curves already in 1815. After him the curve bears the name of Bowditch curve Another name that I found is the play curve of Alice The curves are constructed as a combination of two perpendicular harmonic oscillations. Patterns occur as a result of differences in frequency ratio (a) and phase (b). At high school we used the oscilloscope to make the curve visible (nowadays a computer would do), by connecting different harmonic signals to the x- and y-axis entrance. The curves have applications in physics, astronomy and other sciences. Each Lissajous curve can be described with an algebraic equation.

36. 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

courbe suivante courbes 2D courbes 3D surfaces ... fractals COURBE DE LISSAJOUS Bowditch curve (or Lissajous curve), Lissajoussche Kurve Autres nom : figure de Lissajous, courbe de Bowditch. Pour les intimes : joue courbe d'Alice. n n n xOy Oy n et projection sur xOy Ox n Si n est irrationnel, la courbe est dense dans le rectangle Si n est un rationnel Courbe q si pour p impair ou pour p pair. q si pour p impair ou pour p pair. On obtient une portion de la courbe du n T n pour n entier pair, et pour n entier impair, Pour n = 1, on obtient les ellipses : Pour a = b et n = 2, on obtient les besaces : lemniscate de Gerono : portion de parabole. Pour a = b et n courbe suivante courbes 2D courbes 3D surfaces ... Jacques MANDONNET

37. 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

Lissajous Explorer 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

38. 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

Image 5 / 7 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

39. 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

Weird Pic Tower of Hanoi Lunar Lander Lissajous Lab ... Mailing List Coming Soon to the BRISTOL Cool Stuff - Lissajous Lab Use the preset buttons to the left or make up your own combination of values to create a pattern you like. (See bottom of page for an explaination of the values) Understanding 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. 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.

40. 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

Figuras de Lissajous (atualizado em 27/06/2001) Programa em Visual Basic http://www.cefetba.br/fisica/NFL/ftp/VB3/Lissajous.exe (12 Kb) http://www.cefetba.br/fisica/NFL/ftp/VB3/VBRUN300.DLL (390 Kb) Cópia para impressão: se você quiser imprimir este roteiro, baixe o seguinte arquivo (formato RTF) e imprima-o a partir de um editor de texto: http://www.cefetba.br/fisica/NFL/fge2/lissajous.rtf x(t) = R x sen( w x t + f x y(t) = R y sen( w y t + f y w f Atividades: p /2 radianos (90 graus). Desafio 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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