# Lissajous curve generator

A former Projects Editor at Make: Magazine, his current clients include Autodesk, Digi-Key Electronics, Adafruit Industries, and Cool Tools. Jan 25, 2019 This is my attempt to build a device that will trace Lissajous curves on a CRT Plan: Feed input from two XR2206 function generator kits into a Lissajous figures with laser and two signal generators. A collection of shapes: Epicycloids, Epitrochoids, Hypocycloids, Hypotrochoids, Farris Wheels, Lissajous Curves, and Rose Curves. 13. APA citation: Russell, R. Turn the TIME/DIV knob to xy . The microcontroller will use this input to compute the coordinates for a Lissajous curve and send them back over serial. Different patterns may be generated for different values of n and c. 4 has to be realized. x = A sin(at + δ) and y = B sin(bt + γ) In Example 1, we saw that the curve was an ellipse. You think it’s way too time consuming to count divisions and so some math? I agree, let’s use a fancy thing called a Lissajous curve . and also can be adjust simply by a function generator. Intell. . Using warez version, crack, warez passwords, patches, serial numbers, registration codes, key generator, pirate key, keymaker or keygen for Lissajous 3D 3. Generating Lissajous Figures Using a PC/Laptop Sound Card: Generating various Lissajous Figures on an oscilloscope make a very interesting experiment. By varying, the parameters and, , it is possible to obtain a variety of Lissajous-Bowditch curves with interesting properties. Dec 8, 2011 And after the Epitrochoids, we're going to see another family of wonderful figures: The Lissajous curves. Here the work is done by Cathode Ray Oscilloscope. The story of how the ABC logo came to be, plus a Shockwave simulator of Lissajous patterns. Observing phase shift with Lissajous patterns With the FG at kHz, set the scope time base to observe 1-5 cycles. It is based on the so-called the Lissajous curve of an auxiliary winding voltage Park components. As noted by The most common use of an oscilloscope is to display one or more signals in the time domain. But it is said that the American Nathaniel Bowditch (1773-1838) found the curves already in 1815. And who doesn't dream of standing right inside one all the time? The boys from Tame Impala certainly do, because some of their concert's light shows consisted of little Core Generator (version 2) Exercise: Implement generator of Lissajous curves with following properties: 1. Now it's easy with ViewPort and the Propeller. Many of her projects feature vintage cathode-ray tubes, which are perfect for displaying Lissajous curves. m-1 and a relative permeability of 1) are inspected with a bobbin probe. For example, here is a Lissajous knot. Emily Velasco thought it’d be fun to build a dedicated Lissajous curve generation machine, and the LissaJukebox is the result. Lots of science fiction movies will show Lissajous Patterns on oscilloscopes as it is a very impressive thing to display. The function generator should be set to generate a smooth curve. Picture should be centered and square shaped on the display. Lesson 25: Parametric Curves. The Lissajous curve generator could be used as a music visualizer by controlling the frequency variable with input from and Analog Shield ADC configured as a beat detector. as three group tested and show the result our information that we got from oscilloscope was acceptable. Get Lissajous Curve essential facts. Some of the most common waveforms produced by the function generator are the sine wave , square wave, triangular wave and sawtooth shapes. It is Siglent's New Arbitrary Waveform Generator. Challenging Atatan kit ! This kit is designed only for watching Lissajous figure with ease !. Another name that I found is the play curve of Alice 1. This phase shift can be measured as the fraction of a cycle delayed times 360. The Lissajous curve for the two outputs (Fig. Fascinating and beautiful graphical representations of three-dimensional spherical Lissajous curves can be generated from these equations: Fig. The dual-channel signals generated by the sound card signal generator can be fed Definition of Lissajous curve in the Definitions. 1008-1009, pp. net. This is a project work on electrical representation on Lissajous figure. rupert. They have a practical purpose in mathematics, but you most likely know them as the pretty graphics that show up on monitors in the background of sci-fi TV shows and movies. Xprotolab Portable - Handheld Pocket Oscilloscope, Waveform generator and Protocol Sniffer Room for improvement: * the little buttons are very functional but the menus take a bit of time to learn (as with any miniature DSO) one little potentiometer or rocker switch plus the buttons would be an excellent addition! Damped Lissajous Curves ♦ 2013-03-04 If two perpendicular pendulums are used to control the movement of a pen, the curve traced out is a so called damped Lissajous curve. The tubes have an external diameter of 22. johngineer. If we change the frequency of one of the two motions, then we get a more complicated curve called a Lissajous figure. Sequences of animated Lissajous curves created electronically, in Hewllet- Packard wave forms generators as input to a Tektronics oscilloscope. Figure 3: Lissajous curve: output parameters of a NDT simulation for the SAX probe in diﬀerential mode (amp, phase and ProjY). If it is irrational, the curve will never close and eventually fill a region. Obviously, a suitable function generator will work. : Experimental Study of Q-V Lissajous Figures in Nanosecond-Pulse Surface Discharges increased, pulsed power sources are more and more widely used In between working on other (far more vexing) problems I have been tweaking a somewhat simpler Processing sketch. That is 45 degrees less than previously. (2) Fig. Wikipedia, “Bandwidth”, “Lissajous curve”, “Rise time” 4. A Lissajous plot is generated by choosing two sinusoids, with arbitrary amplitude, phase, and frequency. 🔗 🎥 Lissajous Curve ported When both pairs of the deflection plates (horizontal deflection plates and vertical deflection plates) of CRO (Cathode Ray Oscilloscope) are connected to two sinusoidal voltages, the patterns appear at CRO screen are called the Lissajous pattern. For most Tek scopes, cranking the time base to the extreme left will place you in the X-Y mode. Vol. sine wave generator. 27 mm and they measure 50 mm length. Optimizing a Rectangle Under a Curve. Four steam generator tubes made in inconel (conductivity of 1 MS. Some simple curves in a plane may be described algebraically by setting up a suitable co-ordinate system in the plane and describing the curve as the graph of a function. i N O T E Two-Dimensional Pendulum Experiments Using a Spark Generator Rand S. Start Stop M= N= delay This animation is based on HTML5 + JavaScript and unfortunately doesn't work in InternetExplorer yet. Run on different page. 1 Lissajous-toric knots: various points of view 1. My dad grew up during the depression and was in the Navy in the tail end of WWII. Post subject: Heathkit IO-10 and Wide Band Oscilloscope Question Posted: May Wed 13, 2015 10:27 pm Member Post subject: Heathkit IO-10 and Wide Band Oscilloscope Question Posted: May Wed 13, 2015 10:27 pm Member Internal Wave Generator Demo by BrownUniversity_ENGN1860 in Science. Circuit Generates High-Frequency Sine/Cosine Waves From Square-Wave Input Direct digital synthesis ICs can convert square waves to sine/cosine waves but their complexity is a disadvantage. Hrinyaaw- if you mean you would like to see a point on the curve traced out, I usually just copy and paste the parametric line, then changed all my "t"s to "a"s and add a slider for "a". This example shows how you can create graphs of Lissajous curves basically. Now let’s try 453 kHz. The general shape of the curve is very much dependent on the ratio between the frequencies ω x ABSTRACT – The article describes a very simple device for laser demonstrationof Lissajous figures with a ratio of oscillation frequencies 1:1. The lissajous3d program allows the plotting of 3 dimensional Lissajous graphics. For each observed curve, we determine the number N x of intersections of the Lissajous curve with the horizontal axis and the number N y of intersections of the Lissajous curve with the vertical axis. The Lissajous curves depend on the ratio a b and in our case the curves represent current dependence between 2 signal generator channels. Just finished a program to display Lissajous Curves on an Oscilloscope. It is much easier in Processing. In mathematics, a Lissajous curve / ˈ l ɪ s ə ʒ uː /, also known as Lissajous figure or Bowditch curve / ˈ b aʊ d ɪ tʃ /, is the graph of a system of parametric equations = (+), = (), which describe complex harmonic motion. This app can be displayed in a two-dimensional curve by Lissajous in th… quotient of integers, such as 1,12) so that the angular frequencies O>x and O>yare commensurable, then the curve is closed and the motion repeats itself at regular intervals of time [1]. The other two examples show the effect of different non-linear behaviour on the line. In this release the user can interact with the following parameters: diﬀerence between two points of the Lissajous curve. Or automatically make a web site gallery of all your Lissajous 3D animations or images in one go scratch. 1. Available signals include the usual sine, sawtooth, rectangle with variable duty cycle, white noise, pink noise, MLS, impulse, and step function. Generator. Lissajous curves take certain common shapes depending on the values of the variables in the expressions. We can connect a function generator to both the x and y axis and begin to draw Lissajous patterns. Cathode Ray How can we use the lissajous figures to study the sound and Consider trying to tune two sine wave generators to give the same frequency. Press any key to stop the generation and save the curve as an image in your sketch folder. Lissajous 7. In this challenge we will use a set of iterative algorithms to draw a honeycomb pattern. magnet. When the constant a is rational, the curve is algebraic and closed. After him the curve bears the name of Bowditch curve. Lissajous figures by kitwallace Jan 22, 2014 A whole cycle of the signal (360°) lasts 4. AIM: The aim of this experiment is to investigate the sum of two simple harmonic motions at right angles – the so-called Lissajous Figures and to calibrate a signal generator using another signal generator as a standard. Overview. The Lissajous macro loads a Generator setup called Lissajous. A variation is the display of signals in the frequency The post Using a scope to display Lissajous patterns appeared first on Test & Measurement Tips. 14. The control valve may be closed when the station is at rest, and upon station startup the ramp generator will cause the valve to open slowly until one of the controllers is in control of the system or until the pump is “floating”—that is, operating at a — In the framework of Eddy Current Testing (ECT), this work presents an automated Eddy Current non-destructive testing method based on geometric features of low definition Lissajous figures. Click here to view all our demos, or click on of the buttons below to browse a specific category. Sinusoidal voltages are applied to the horizontal and vertical deflection plates, they have the form V = A Mar 29, 2010 As part of the Excel Lissajous Curve Explorer I have included a gallery that you . You can just run its screen saver to enjoy the patterns - or generate new ones of your own and export them as images, movies or 3D animations. What is the phase shift at kHz? The Lissajous curves could be produced by harmonographs (an apparatus that has a pendulum with some writing device attached to it), or on oscilloscopes, where the horizontal and vertical electromagnets would drag the electron beam along the screen. However, the signal L-Scope is a real-time audio visualizer that works within M4L and acts like an oscilloscope in XY mode and reacts with any given audio input signal. net/lissajous/) allows controls for A and B as integers from 1 to 12 each. Select your F-curve then press N on keyboard to open the properties panel: This example shows the built-in sine function. Description. To study the series and parallel LCR circuit and plot the resonance curve at the… Lissajoux 1. A Lissajous curve is formed when two sine waves plotted on their respective X and You can see one using an oscilloscope and a couple of signal generators, How to draw 2D oscillations and Lissajous curves using. http://micro. Aug 28, 2018 Lissajous figures are built from parametric equations. In mathematics, a Lissajous curve also known as Lissajous figure, is the graph of a system of parametric equations [17]. Oct 9, 2010 LISSAJOUS - a simple example of 2D line plot in Matlab, and creating a GUI without GUIDE. au/tutorials/processing/examples/Lissajous Free online 3D grapher from GeoGebra: graph 3D functions, plot surfaces, construct solids and much more! Lissajous curves of the welded part of the U-rib with different length cracks. Lissajous 3D can make many beautiful relaxing animations. Siglent’s new arbitrary waveform generator. This matrix is disassembled into X Y pairs by In this paper, a new method for doubly-fed induction machine electrical faults diagnosis is presented. by This littleBits project generates Lissajous curves taken from the idea of the Etch-a-sketch project that comes in the 1102 H. El Menzhi and A. oscilloscope and looking at my function generator and the python interface I have to it. That means that the change in phase difference (ΔΦ) is about 15° per 1 kHz change in frequency (Δf). 1039-1051, 2014 L. 8, No. Hello we wanted to find the angle difference of two analog input signal in my university lab. de. Jules-Antoine Lissajous (1822-1880) discovered these elegant curves (in 1857) while doing his sound experiments. edu A method is proposed to determine lifetime of luminescent emissions based on the phase shift measurement employing the digitalized Lissajous representation: this diagram has been typically used with analogical algorithms, whereas the proposed method is performed in digital domain, showing an improved accuracy and repeatability. made with graphics explorer a functions and equations grapher program. NI, Labview Basics 1 – Introduction, Course Manual 5. 3. First Prize 53 5. Lissajous curves have applications in physics, astronomy, and other sciences. but we have a important question that one of the other group asked us. This allows you to see a continuous change of a Lissajous curve, while you alter m,n or the phase. 4. 1 A description Interactive installation composed of a blood pressure meter connected to a lissajous curve generator, which generated curves taking as imput values the measures of systolic and dyastolic pressure of the visitors. A ramp generator is used for ramping the control valve to a new position. ) The signal function generator is an electronic device which produces waveforms. Lissajous curves (Interaktiivinen Lissajous'n käyriä generoiva JSXGraphia käyttävä Javascript-applet) jsxgraph. If you are tuning audio filters Lissajous can easily and accurately get them on frequency. One can easily find that the 3-D Lissajous curve is located in plane A. dependent transfer of linear systems, investigation in time domain, (3) signal shaping in distributed parameter systems, (4) averaging as noise suppression. Lissajous pattern can be easily generated by making two function generator in LabVIEW and then from both function generator apply signal to X channel and Y channel respectively. 1%. But enough for us to have fun producing Lissajous curves! Lissajous Curve Generator. Curve Sketching, Geometry, Parametric Curves, Polygons, Trigonometry This is a collection of graphs that are great to plot with an AxiDraw. Measurement of phase difference between two signals using dual beam CRO. The parameters RT and LT describing plane A can be computed using three measurement points (say points a1, a2, and a3 in Fig. the Lissajous curve on the top trace would be a simple sine wave with half the frequency of the blue trace. A & B refer to amplitude (the length pendulum travels before reversing its direction) along X & Y axes PROCEDURESPART A : FREQUENCY MEASUREMENT USING LISSAJOUS FIGURES 1. We will develop more general methods of converting roulettes into SVG, including Lissajous Figures and Farris Wheels. id. More coming soon ! quotient of integers, such as 1,12) so that the angular frequencies O>x and O>yare commensurable, then the curve is closed and the motion repeats itself at regular intervals of time [1]. They can be seen on oscilloscopes when 2 signals are mixed. Explore math with desmos. To view this page, you need a plug-in called Shockwave that you can download free from the web. A simple Lissajous curve in itself soon gets visually boring, but the nature of mechanical pendulums which are subject to friction inevitably implies decaying amplitudes so figures traced gradually reduced in size and the overlapping lines increased the visual appeal. Picture is generated on analog VGA monitor (you can use 640x480 mode). Introduction What are Lissajous Patterns? Lissajous Patterns are the result of two sine waves controlling the X and Y axes of an oscilloscope. Artif. On 19 February 2018, ABC The Lissajous Curve Thingy Films created its new logo. ) In the example in Curvilinear Motion, the Lissajous figure Lissajous curves in vivo To get a better understanding of the Lissajous curves the choice "move Lissajous curve" was introduced. If a is irrational, the curve fills the area [-1,1] x [-1,1]. : The Lissajous Curve Thingy Company, Inc. 3K Lissajous Curve Apparatus by JavierL90 in Science. They have a practical… Jul 8, 2019 an extraction technique of the crack signal using the Lissajous curve of the 5 V, and the induction coil was operated by a function generator. Calculate the frequency 𝑓1= 𝑁 𝑁 𝑓2 and the angular frequency 𝜔1=2𝜋𝑓1 of the signal from the generator G1. Abstract. Lissajous Figures . #49: Simple Component Tester using Oscilloscope - Octopus Curve Tracer Choosing a Backup Generator Plus 3 This video takes a fairly detailed look at the basics of Lissajous patterns on an Lissajous curves are the family of curves described by the parametric equations x(t) = a sin(nt +c) y(t) = bsin(t) The curves are named after Jules-Antonie Lissajous (1822-1880) who discovered the curves (in 1857) while doing experiments involving sound vibrations. Assumed that it has correct dial markings. Sinusoidal voltages are applied to the horizontal and vertical deflection plates, they have the form V = A sin(ω t + φ), where A is the amplitude, ω is the angular frequency and φ is the initial phase. This Frequency Measurement by Lissajous Method techniques used are simple and dependable, and measurement may be made at any frequency in the response range of the oscilloscope. This document covers four methods and summarizes the advantages and limitations of each. Lissajous Curve Generator (version 2) - OpenProcessing Lissajous Generator¶ class scanpointgenerator. (a) Lissajous curve of the non-crack area. For this purpose, time domain mathematical model of a three Dec 18, 2012 The patterns, called Lissajous Figures, are generated using a laser and 2 motors with mirrors attached to them. Also the electric circuit for quick and convenient demonstration on the screen of an oscilloscope of Lissajous figures with different ratios of oscillation frequencies is described. In this demonstration we look at curves of A designer might drag an icon of a sine wave generator into a design area, drag an oscilloscope into the design area, then wire them together by dragging a Jan 11, 2016 Chilling inside a giant Lissajous curve with WebVR Tame Impala certainly do, because some of their concert's light shows consisted of little else than Lissajous curves: SEven – A Science Fiction Event Graph Generator I remember making interesting Lissajous figures in a physics class years ago. BENOIST Commissariat h l'Energie Atomique, Gif-sur-Yvette P. inputs. e measurement of phase difference and frequency using CRO which are Lissajous patterns. You can save movies, or images in many formats. In mathematics, a Lissajous curve is the graph of a system of parametric equations. Measuring relative phase between two waveforms using an oscilloscope Overview There are a number of ways to measure the phase difference between two voltage waveforms using an oscilloscope. A Lissajous pattern is a graph of a curve in which both the x and y Cartesian coordinates are periodic functions of time (t) given by equations — typically, x = sin(nt + c) and y = sin(t). Changes for this version include the line gradually changing colors, centering the curve around the mouse position, and clearing the screen when the mouse button is clicked. Lissajous v37. Oct 26, 2017 A Lissajous curve can be calculated using x(t) = sin (2π fx · t + φx) and y(t) = sin ( 2π fy . Now set up for additional Lissajous figures using the 60 Hz transformer output for the Ch 1 scope input and and a sinusoidal output from the function generator for the Ch 2 scope input. Lissajous figures by kitwallace, published Jan 22, 2014 . From JSXGraph Wiki. Procedural terrain generator. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1. X on the input, Y on the output. Lissajous curves using a differential vector and the same data from Fig. Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations However, most oscilloscope will allow you to supply an external input that will allow you to directly control the x axis. J. Google "Lissajous curve" and "phase shifter". View Videos or join the Lissajous Curve discussion. Interactive Lissajous curve Aug 11, 2016 lissajous patterns. Lissajous Curve Explorer : Figure Eight : Moon Phases Simulator : Flat Map Component : Sun Motion Question Checker : Solar Neighborhood Demo : Parallax Demo : Parallax Explorer : SN Test : Terminator Demo : SN Light Curve Fitting Explorer : Daylight Hours Explorer : Airy Disc Experiment : Tracks Test : Stellar Evolution Test : Aberration Faculty of Engineering Chulalongkorn University Cathode-Ray Oscilloscope (CRO) Objectives You will be able to use an oscilloscope to measure voltage, frequency and phase on a variety of displayed waveforms Introduction The oscilloscope is the basic instrument for the study of all types of waveforms. Lissajous curves are graphic patterns that can be obtained through the parametric equations: x(t) = A sin(at+δ), y(t) = B sin(bt) The curves describe harmonic vibrations. GEN, and by default starts with Y set to Left Out and X set to Right Out, each at 100 Hz but with Left Phase set to 45 degrees. A Lissajous curve is formed when two sine waves plotted on their respective X and Y axes. Spectrum Analyzer with different windowing options and selectable vertical log. It's completely free, and there's no need to register or sign-in. The most basic use of them is as the phase-space plots of harmonic motion in multiple dimensions. The film is a This is simply to prove to myself that I could make lissajous figures in . Set the function generator to 30 Hz. to get a Lissajous curve pattern on your scope, you need to set the horizontal input to external, feed a sine wave signal into the vertical input and a sine signal (of the same phase) into the horizontal input. See more ideas about Sound sculpture, Sculpture and Sound art. The geometric construction. Ultimate Tic-Tac-Toe is a 2-player computer game played on a game board comprising nine tic-tac-toe games set out in nine mini-squares within a 3x3 greater-square. Lissajous is a tool for programmatic audio performance in the browser using Javascript. (The laser source can be a These patterns are called Lissajous figures and are a common means of comparison wherever an accessible frequency standard (signal generator) exists . ’s film distributing division. Maybe many people try to see Lissajous figure preparing 2 sine-wave oscillators and an oscilloscope with XY input. This article presents a group of shapes that you can use in your applications. In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations{\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt),}which describe complex harmonic motion. In a typical, male-dominated, Chauvinistic manner, this article from the March 1957 edition of Popular Electronics delves into the subject of Lissajous patterns. Lissajous pattern generator for beginners by WillemvD is licensed under the Creative Commons - Attribution - Share Alike license. Additionally, the generator can provide a musical scale progression, as well as frequency sweeps for periodic signals. Spherical double Scotch yoke is a relatively simple mechanism, complying with this requirement and realizing the required figure-of-eight as a spherical Lissajous' curve. Lissajous figures are parametric curves where both x(t) and y(t) are sine functions. . A and B represent Lissajous figures are parametric curves where both xt and yt are sine functions If the ratio of the frequencies is rational the curve will always eventually close If it The Lissajous curves are the trajectories of a point the components of which have a sinusoidal movement. Procedural terrain generator for Unity3D. Oct 31, 2016 Lissajous Curve Generator in C#. These can be generated in a variety of Jan 9, 2014 It seems that both x and y have an offset, since a Lissajous curve should oscillate around the origin, so: x=Asin(at+δ)+x0 and y=Bsin(bt)+y0. Some of these patterns are shown in fig. com, a free online graphing calculator Yes, by using F-curve modifiers. com, a free online graphing calculator Lissajous Curves. Contribute to wespo/Lissajous_curve development by creating an account on GitHub. Lissajous Curve Table. We can generate these curves in Excel by using below equations. The number signals can be varied by using different frequencies and amplitudes. See the beauty of math in Lissajous curve also known as Lissajous figure or Bowditch curve is the graph of a system of parametric equations which describe complex harmonic motion. In mathematics, a Lissajous curve / ˈlɪsəʒuː /, also known as Lissajous figure or Bowditch curve / ˈbaʊdɪtʃ /, is the graph of a system of parametric equations Get the free "Lissajous Curves (Harmonograph)" widget for your website, blog, Wordpress, Blogger, or iGoogle. It consisted of a vibrating tuning fork to which a mirror was attached. What does this mean? Remixing or Changing this Thing is allowed. TL071 datasheet 3. This is an article about Lissajous Curves. Then the resulting path is called a Lissajous curve. I constructed a basic Octopus after reading an article published by David Ludlow, W7QHX, in QST. The offset angle determines the phase shift of the coordinate of the red point of the upper left wheel and affects the shape of the Lissajous figure generated. A generator is coupled to a bicycle mechanism, so that a person can generate their own electricity: Generator Load The person pedaling this bicycle/generator notices that it becomes more diﬃcult to pedal when the generator is connected to a load such as a light bulb, or when it is charging a battery. Used part of Johngineer's www. • Phase-shifter circuitsare in cardboard box in the cabinet nearest to the door. Two signal generators was used and the first generator (generator 1) was considered as the known or standard frequency source. Such a curve is generally known as a Lissajous figure or Bowditch curve. These values can then be used to dynamically plot the curve. An example Lissajous curve for a 300 MVA transformer is plotted in Fig. Drag to change the angle of viewing. (b) Lissajous curve of the 10-mm length crack. Sinusoidal Jules Antoine Lissajous was a French physicist who lived from 1822 to 1880. • Remember to set HIGHZmode on function generator. Jump to: navigation, search. Each channel has a variety of individual controls which affect how the channel's input will be processed and displayed on the screen. 4) indicates that the phase circle matches the 89. An oscilloscope, previously called an oscillograph, and informally known as a scope or o-scope, CRO (for cathode-ray oscilloscope), or DSO (for the more modern digital storage oscilloscope), is a type of electronic test instrument that graphically displays varying signal voltages, usually as a two-dimensional plot of one or more signals as a function of time. Lissajous Figures 1. It is easy to see that the This littleBits project generates Lissajous curves taken from the idea of the Etch-a -sketch project that comes in the LittleBits Arduino starter kit. The patterns generated by sand pendulum are nothing but Lissajous curves. Find more Mathematics widgets in Wolfram|Alpha. Ultimate TicTacToe. When it is a rational number, a closed curve is generated; when it is irrational, the curve never closes and fills the square. 125 divisions between the two signals. Info on the software including a demonstration video and a link to the PDF manual can be found here: Frequency Measurement by Lissajous Method: The oscilloscope is a sensitive indicator for frequency and phase measurements. sine-wave generator Lissajous curve. It is a very important oscilloscope used to analyse the waveform and measure them. Function generator generates waveforms such as sine waves, sawtooth, triangular and square waves. Lissajous is a planar figure obtained by combining two single vibrations vibrating in directions perpendicular to each other. Bézier curves are used to draw smooth curves along points on a path. 6. Two lines are drawn, one horizontal and the other vertical so that they do not pass through any intersection of different parts of the Lissajous curve. Use signal generators and an oscilloscope to generate lissajous figures Alternating Current Generators. 1 My device nicely accomplished the job with its single output of 1 all unnecessary cables from the equipment V limited to 1 mA. The frequency of the standard oscillator is driven by the second channel of the oscillator Also you can make curves that spiral around themselves as they trace the Lissajous curve. Lissajou Curves. 2. Saad, "Lissajous Curve of an Auxiliary Winding Voltage Park Components for Diagnosing Induction Motor Inverter Defects", Advanced Materials Research, Vols. 3D projection. We have seen already how useful such a description is; for example, we used it to obtain a formula for the arclength of such a curve. There are several ways of describing them. The fill factor was LISSAJOUS - a simple example of 2D line plot in Matlab, and creating a GUI without GUIDE. About Donald Bell Donald Bell is the creator of Maker Project Lab and the weekly video series Maker Update. Lissajous figures. [Update: Many of you have been using Mac's Grapher… A similar thing can . html. Most of the graphs are dynamic, giving you multiple opportunities for customization. Coding Challenge #116: Lissajous Curve Table In this Coding Challenge, I visualize a "Lissajous Curve Table" with Processing (Java). uni-bayreuth. Not being a precision laboratory instrument, the signal generated was occasionally jittery. He was a prominent and successful lecturer, demonstrating a device he built which generated these patterns. 1039-1051, 2014 Lissajous figures also called Bowditch curve, pattern Generator. Co, Brooklyn, N. Open the console to start Lissajous. A quick sketch that generates a Lissajous Curve using two randomly selected numbers from 0-10. Low poly house made with Blender3D. Lissajous curves are given by the two parametric equations shown here. js library. The model with the curve's coordinates. Oscilloscopes; Lissajous Figures. The output of each is sampled byt the jit. 0 Lissajoux is a animated Lissajous figure controller. com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. Lissajous curve. 0 license key is illegal and prevent future development of Lissajous 3D 3. 0. Due to the phase difference between voltage and current, we will see an ellipsis or sometimes a circle with a perfectly smooth curve. Retrieved October 26, 2019, from http://www. That method was fairly specialized, not suitable for other Photographer when I can, Programmer always. These elegant curves, C. Some months ago I watched Brendan Dawes' talk at TEDx Manchester in which he uses Lissajous curves to get at the value of iteration in design. Blast! your browser is so old it does not support HTML5! Blast! your browser is so old it does not support HTML5! δ = 0 Click on the graph to save this lissajous as an image The easiest way to demonstrate Lissajous Pattern in class is to use a sound card oscilloscope and signal generator. They will get acquainted with time domain reflectometry, and practice the time and phase measurement with oscilloscope, and failure diagnosis by means of investigation of time domain waveforms. Curves are drawn in square field of 384 x 384 pixels. In mathematics, a Lissajous curve (Lissajous Lissajous is a complex audio/video signal generator built in Max/MSP and inspired oscillations as XY matrix functions and creates complex graphics curves. Lissajous curves are fun. A Lissajous curve, named after Jules Antoine Lissajous is a graph of the following two parametric equations: x=Asin(at+ϕ)y=Bsin(bt). Faculty of Education, Masaryk University, Brno. But this The curve generates pitch, harmonics and volume of sound. 7K In physics and mathematics, the phase of a periodic function of some real variable is the relative value of that variable within the span of each full period. A Bézier curve goes through points called anchor points and the shape between the anchor points is defined by so called control points. Or export 3D animations in Obj format to import into other 3D programs. This is a support page to the multimedia chapter Interference and Consonance in the volume Waves and Sound. This ux in the coil is given Sine wave synonyms. 125 divisions. Honeycomb is a structure of hexagonal cavities (cells of wax), made by bees to store honey and eggs. The kinematics of an insect-like flapping wing for MAVs requires three-dimensional motion which is essentially spherical in character. The function generator is set to a square voltage with a frequency of about 100 Hz. If you add a z coordinate also given by harmonic oscillator. com topic list or share. They were first discovered by Nathaniel Bowditch and later investigated by Jules Antoine Lissajous. – Use Lissajous ﬁgure handout to help decipher ﬁgures — make sure your angles are in the correct quadrant (hint: probably quadrant III — between 90 and 180 of phase delay). 2 Input parameters and associated random distributions deﬁnition By relying on both expert reports and data simulations, the set of the in- Helping Hands For Laser Lissajous Rough Draft #Lissajous curve project drawing Web Audio API to turn a cell phone into a crude 2-channel function generator. Plan: Feed input from two XR2206 function generator kits into a small stereo amplifier board, and send the output from the amplifier into the X and Y deflection coils of a small CRT. A function generator is usually a piece of electronic test equipment or software used to generate different types of electrical waveforms over a wide range of frequencies. Generate the points of a Lissajous curve A Lissajous curve is formed when two sine waves plotted on their respective X and Y axes. A full list of all our computing challenges organised in categories: BBC micro:bit, Python, HTML/CSS, Javascript and Computing Concepts. by Nathan Balk Simple HTML5 Lissajous curve generator HTML55 Lissajous (Demonstraatio, jossa arametreille a ja b voidaan valita mikä tahansa kokonaislukuarvo 1:n ja 12:n väliltä) devadutta. Matías,andFranciscoJ. These are input coupling, vertical position, and volts per division (these switches are found above their corresponding input channel). Now here we will discuss how the measurement of waveform i. The inflection points on the curve create rhythmic structures. Pergamon 0952-1976(95)00011-9 Engng Applic. For example after selecting "move Lissajous curve" choose m=5 n=6 and change the phase via the slider. Arbitrary Waveform Generator with Sweep on all parameters. When the generator providing feature of the signal generator as well as its offset manipulation feature. The size (amplitude) of the curve corresponds roughly The Lissajous-Generator allows the creation of three-dimensional figures by entering a few parameters. Lissajous curves. Lissajous Curve Table simulation made in Javascript using p5. If you want to see the Lissajous' actually "rotate" you need to have the two generators within a VERY FEW, maybe 5 or 10 cycles of each other and as Walter says you can easily display some simple, small ratios. sinusoidal curve. 3 Voltage-time curve of a capacitor for incomplete charging and discharging. If you use a linear test load like an R-C or R-L or just C or L then you will get an ellipse displayed and that is a perfectly valid Lissajous curve, see the Wiki page for an animation. Named after Jules Antoine Lissajous, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous . 2). One sinusoid becomes the value of x(t), and the other becomes y(t); the resulting Lissajous curve is the result of plotting the (x,y) points for a continuous range of times. Look below to see them all. Examples of the Lissajous curves L. Lissajous Box consists of two speakers with a mirror mounted on each speaker so that one mirror swings Lissajous curves are the mesmerizing result of graphing two functions, one on the X axis and one on the Y axis. In mathematics, a Lissajous curve / ˈ l ɪ s ə ʒ uː /, also known as Lissajous figure or Bowditch curve / ˈ b aʊ d ɪ tʃ /, is the graph of a system of parametric equations. The simple rule mentioned above needs following modifications. A Lissajous curve, named after Jules Antoine Lissajous is a graph of the following two parametric equations: (1) x = A s i n ( a t + ϕ ) (2) y = B s i n ( b t ) A and B represent amplitudes in the x and y directions, a and b are constants, and ϕ is an phase angle. This means that if we project a Lissajous knot onto a coordinate plane, we get a Lissajous curve. Sep 26, 2016- Lissajous curve /ˈlɪsəʒuː/, is the graph of a system of parametric Lissajous curve - Wikipedia Sound Design, Function Generator, Gaming, It also explores the derivative curve of a Lissajous curve which is another Lissajous understanding it is possible to plot these curves on a graphing calculator. Previously, a method was described for converting standard spirograph shapes (hypotrochoids and epitrochoids) into SVG using a Bezier curve-fit method. JAN VÁLEK, PETR SLÁDEK. But if we are try to do this with the help of DAQ then we face the problem of acquiring multi channel. See the code at the bottom for Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers Summary Sophisticated calculators have made it easier to carefully sketch more complicated and interesting graphs of equations given in Cartesian form, polar form, or parametrically. I have played around with PC software (Tone Generators) that will output to LEFT/RIGHT channels and you can play with the frequency, phase and amplitude, and choose between sine,square and triangle waves. A cell phone running simple tone generator app provided input signal. Sep 26, 2016- Lissajous curve /ˈlɪsəʒuː/, is the graph of a system of parametric equations which describe complex harmonic motion x=A\sin(at+\delta),\quad y=B\sin(bt) This family of curves was investigated by Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857. edu/electromag/java/ generator/ac. Discrete Lissajous Figures and Applications In mathematical 29 terminology, a Lissajous curve is a simple system of two 35 curve is highly dependent on the ratio b/a, and also on the 36 phase LittleBits Lissajous Curve Generator. Printed in Great Britain Contributed Paper Expert System for the Characterization of Defect Signals in Steam Generator Tubes B. Lissajous figures are produced in two dimensions when the x and y coordinates are given by two sine waves, which may have any amplitude, frequency and phase. The Lissajous- Bowditch curves are generated by a parametric representation in the time variable of the two sinusoidal functions . by Suzanne von Oy. exp. You may remember Velasco from her Freeform Mini CRT Sculpture that we featured a few months ago. An excellent example of parametric curves can be found in the example of a Lissajous figure. Animated Lissajous figures. Worland, Department of Physics, University of Puget Sound, 1500 North Warner, Tacoma, WA 98416; Physics at school - HTML5 (Physics Animations/Simulations) Mechanics Gravitational field Mechanical vibrations and waves Molecular Physics and Thermodynamics Electrostatics Electric current Semiconductors Electric current in liquids Current conduction in gases and vacuum Magnetic field Alternating current Optics Special relativity Atomic physics Nuclear physics Mathematics The third one is a Lissajous curve with a frequency ratio of f 1 /f 2 A connectionist central pattern generator for the aquatic and terrestrial gaits of a interface with the function generator and the circuits we build. If the “X-Y” button is on, the horizontal deflection (X) of the electronic beam drawing the curve is not controlled by the sawtooth generator of the oscilloscope but by the signal attached to channel 2. About: Beyond simple math and grouping (like "(x+2)(x-4)"), there are some functions you can use as well. z(t) = cos(n z t + φ z) then the result is a Lissajous knot. Greetings all. Note that signal across the capacitor lags the signal across the function generator. which describe complex harmonic motion. The Generator option allows definition of a custom function like the damped sine. The media project is born with the purpose of investigating the relationship between sound and vision, chaos and order, closely related to astronomy, mathematics & physics. Generator 2 will be the variable (unknown) source. Observe the Lissajous patterns for function generator frequencies of 20, 30, 60, 120, and 180 Hz. completing the measurements, the Lissajous curve on the screen should be moving. Mike Lissajous Art Peter Elsea 11/26/08 2 Figure 1 is a basic Lissajous generator. ). Contribute to niewicz/lissajous development by creating an account on GitHub. If A ≠ B and a = b, we obtain an ellipse. PIGEON Commissariat ~ l'Energie Atomique, Gif We study a class of knots generalizing torus knots, which we call Lissajous-toric: a torus knot is generated by a a circle rotating around an axis and a Lissajous-toric knot is generated by a Lissajous curve rotating around the axis. The phase is typically expressed as an angle (), in such a scale that it varies by one full turn as the variable goes through each period (and () goes through each complete cycle). php Fig. (Python) Trouble displaying a graph of a Lissajous curve Lissajous figures are such fun and educational little "toys. Your design thinking is good because you can "drive" the component under test at any frequency up to the bandwith of you drive amplifier and so you are not ABC The Lissajous Curve Thingy Films was created on 31 January 2017 as ABC L. Interactive Lissajous curve generator – Javascript applet using JSXGraph; Animated Lissajous figures; ABC (Australian TV channel) ABC (formerly known as The ABC National Television Service or ABC-TV from 1956 until 2008, and as ABC1 from 2008 until 2014) is a national public television network in Australia. THEORY curve tracer, analog signature analyzer, component tester, oscilloscope test adapter, or simply “Octopus”. 22 mm, an internal radius of 9. Simple HTML5 Lissajous curve generator (http://devadutta. As a 20th-century student of physics, I was introduced to Lissajous curves in an electronics lab. Apart from that, these curves are of particular value in electronics, serving to identify the characteristics of any unknown electric signal when compared Lissajous figures are created by combining a periodic motion in one direction with a periodic motion in a perpendicular direction. EXPERIMENTS BASED ON CRO The wave shapes analysis, measurement of frequency and voltage values (peak to peak and RMS) at different ac. You can change the amplitude, frequency and phase shift between the X and Y channel. 309-318, 1995 Elsevier Science Ltd. catch~ object and stuffed into a 2 plane matrix. We determine the frequency f 1 of the signal coming from the examined generator: 1 N f 2 N f x y. In fact, we had to turn the volume down to almost minimum for tonight’s experiments. In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of a system of parametric equations: x=Asin(at+d) y=Bsin(bt) which describe complex harmonic motion. The macro also invokes the _Liss_Ctrls macro to use the Custom Controls dialog for easy experimentation with frequencies and phase. They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857 (MacTutor Archive). GAILLARD URA CNRS 817 HEUDIASYC, Compiegne M. 84 mm, a thickness of 1. The Lissajous patterns for other frequency ratios can be similarly drawn. Most dual trace scopes have the capability of X-Y traces, as well as many vintage scopes. Top synonym for sine wave (other word for sine wave) is sinusoidal wave. Combined with a two-channel waveform generator, a full spectrum of excellently stable Lissajous figures can be generated (concerning frequency ratio, amplitude ratio and initial phase angle difference). Adjust the gains until you get a nice even circle displayed on the screen. Repo here. Horizontal and Vertical Cursors with automatic waveform measurements. 22 3. Cite As Maciej Kalarus (2019). Connect the two function generators to the oscilloscope via the output socket to Concept: A Lissajous curve is the graph produced by two phase-shifted scanning probe is usually presented in the complex plane as a Lissajous curve . Signal Generator The signal generator panel is small but busy (see Figure 2). AC Circuits . One connected two signal generators, each making a voltage May 10, 2016 An Optimized Method Based on Digitalized Lissajous Curve to . They are mostly standard functions written as you might expect. What does Lissajous curve mean? Information and translations of Lissajous curve in the most comprehensive dictionary definitions resource on the web. (3) Lissajous Curves: Earlier in this course, we've encountered Lissajous curves. When the periods of motion in the two directions make a simple ratio, then a closed curve results. Lissajous is a complex audio/video signal generator built in Max/MSP and inspired by the work of Jules Antoine Lissajous. In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous ﬁgure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations which describe complex harmonic motion. Sine wave synonyms. Sign in / Join. Click to load samples. The Lissajous curves of parameter n (ratio between Lissajous curves (sometimes also known as Lissajous figures or Bowditch we were taught about Lissajou using oscilloscopes and two signal generators. Low poly house. (See more on the Ellipse. A simple Lissajous curve generator. Jiang et al. The vertical deflection (Y) is determined by the signal attached to channel 1. Summary: Siglent's new arbitrary waveform generator is a pro-level instrument for a (well-off) hobbyist price. classification of magnetite buildup in PWR steam generators”, in Review of the ratio of the frequencies of the oscillations, and a Lissajous figure is born! Now, these figures don't necessarily have to be created by just two pendulums. Hence, the differential parameters of a dual-channel magnetic sensor have been used for the Lissajous curve to reduce the magnetic noise and discriminate the crack signal from the liftoff signal . In our experiment we had to show the practical representation of Lissajous curves on the oscilloscope display. Calculate for each frequency f 2 the number of intersections of the Lissajous curve with the N x and N y axes. X = A * SIN(a*t + d) Y = B * SIN(b*t) where. Hz with a wave generator Tektronix CFG280 by a 1 V peak to peak sinusoidal Aug 10, 2013 2-channel frequency generator to create Lissajous patterns - Page 1. [2] Transformers are used to raise or lower AC voltages. Here it is with some of the more elaborate settings to transform the Lissajous patterns, such as textures, clipping of the curve and so on: Virtins Sound Card Signal Generator; The dual-channel off-line Oscilloscope provides four types of views: (1)Wave form display of Channel A and Channel B (2)Wave form display of Channel A + Channel B (3)Wave form display of Channel A - Channel B (4)Lissajous Pattern display for Channel "Sound Lissajous Meter" is a new sound analysis app that displays audio signals in Lissajous curves. In Pipeline Rules of Thumb Handbook (Eighth Edition), 2014. Of course that was 30-something years ago when I was first getting into electronics and electricity, but even today it's a cool thing to do. A fourth of it (90°) would be 1. fsu. As there is a provision of We have already discussed Cathode Ray Oscilloscope or CRO. Oct 11, 2019- Explore rickdrako's board "Sound Sculpture" on Pinterest. You will notice that unless you get the frequency set exactly The Lissajous curve using the parameters of a single sensor is easily affected by the magnetic noise and the liftoff signal. (2016, July 05, 07:47 am). Meaning of Lissajous curve. 1° reading in Figure 3. L-Scope comes as part of the Lissajous M4L & Standalone Bundle and can be purchased HERE. The projection of a Lissajous knot onto any of the three coordinate planes is a Lissajous curve, and many of the properties of these knots are closely related to properties of it. Retrieved October 11, 2019, from http://www. The equations that describe these Lissajous Figures. Then you can play the slider and the point will travel along the curve, "tracing" it. Connect the AC transformer to CH1 and connect the function generator to CH2 under the VERTICAL section. The lecture on graphing and this graph are very impressive. At XY Mode (Plot Lissajous patterns or see the phase difference between two waveforms). Each cycle~ object is independent with controls for frequency, phase and amplitude. Amongst other things, this is useful for examining signals in an oscilloscope - by comparing the Lissajous figure the oscilloscope generates with a chart, you can compare the frequencies and phase differences of different signals. Using a Krohn-Hite 6900B distortion analyzer and a 1-MHz Krohn Hite lowpass filter (to remove the clock), the circuit’s total harmonic distortion on the sine output was only 0. 5 divisions. 1. sketches of their Lissajous figures, which are produced by means of a sine/ square wave generator, Eico Electronic Instrument. " I demonstrate them as soon as soon as I introduce AC circuit theory in my classes. You can see one using an oscilloscope and a couple of signal generators, if you play with one of those Lissajous curve explained In mathematics , a Lissajous curve , also known as Lissajous figure or Bowditch curve , is the graph of a system of parametric equation s x = A\sin(at + \delta), y = B\sin(bt), The goal here is to create a self-contained "appliance" that will draw Lissajous curves while using as many off-the-shelf items as possible. musical intervals and vibrating strings · Interactive Lissajous curve generator – Javascript applet using JSXGraph; Animated Lissajous figures Lissajous curve. (2016, July 05, 07:26 am). au/tutorials/processing/examples/scintillating. Measurement of frequency using Lissajous figures. net dictionary. On the oscilloscope, there should be a rapidly changing display on the screen. Introduction. Hi, I wanted to make a simple hardware device to create Lissajous patterns. Simple HTML5 Lissajous curve generator HTML55 Lissajous (Demonstraatio, jossa arametreille a ja b voidaan valita mikä tahansa kokonaislukuarvo 1:n ja 12:n väliltä) devadutta. wrote a program to graph Lissajous curves but for whatever reason when the graph is shown it's blank. mit. He had little use for Japanese products, and to this day sniffs at anything from China. com christmas tree code and design to help with the x-y vector control of the oscilloscope. Interactive Lissajous curve generator - Javascript applet using JSXGraph; Animated Lissajous figure maker. Y. The curves close iff is rational. Method Oscilloscope Requirements Waveform Requirements In mathematics, a Lissajous curve / ˈ l ɪ s ə ʒ uː /, also known as Lissajous figure or Bowditch curve / ˈ b aʊ d ɪ tʃ /, is the graph of a system of parametric equations = (+), = (), which describe complex harmonic motion. An Optimized Method Based on Digitalized Lissajous Curve to Determine Lifetime of Luminescent Materials on Optical Fiber Sensors AdriánRidruejo,NereaDeAcha,CésarElosúa,IgnacioR. Lissajous curves (sometimes also known as Lissajous figures or Bowditch curves), are pretty shapes first investigated by Nathaniel Bowditch in 1815, and later (and in much more detail) by Jules Antoine Lissajou in 1857. Top synonyms for sine wave (other words for sine wave) are sinusoidal wave, sinusoidal waveform and sinusoid. By shifting the frequency and phase of the signals, you can get different shapes. But usually, after short time, the show is over because of a mess of wiring and not stable situation of wave form. German Mit dem digitalen Lissajous-Generator lassen sich räumliche Figuren durch Eingabe einiger Parameter erzeugen. microcontroller implementation of digital pid controller measuring phase and gain margin by lissajous curve 19 -20 us ing signal generator 2. how can i generate a circular waveform on an oscilloscope using function generator? circular waveform using oscilloscope org/wiki/Lissajous_curve . Lissajous is here! Audiobulb is extremely excited to announce the release of Sineraw's amazing new audio visual software generator. REFERENCES 1. Boylestad & Nashelsky, Electronic Device and Circuit Theory, 2006 2. A collection of interactive, educational demos and tools. Determination of B-H Curve of Core Material of Transformer 1 Aim To determine of B-H curve of core material of transformer 2 Theory The rms voltage induced in a transformer is given by E= 4:44˚ mfN (1) where, ˚ m is maximum value of the ux in the core, fis operating frequency and Nis number of turns in the coil. A Lissajous curve can be calculated using x(t) but the phases does not affect to resonant operation of micro-scanners and also can be adjust simply by a function generator. ” I don’t always blog about figures, but when I do, they’re lissajous Academo. Lissajous Figure Generator Tue 28 February 2012 One of the more difficult concepts for my ECE207 students to understand is that of using the oscilloscope in XY mode to view Lissajous figures. In eddy current testing of heat-exchanger pipes the signal of the scanning probe is usually presented in the complex plane as a Lissajous curve. Measurement of the time constant using the oscilloscope For the determination of the time constant RC with an oscilloscope a RC circuit as shown in Fig. Pendulum pattern – Lissajous curve. 8. You can see one using an oscilloscope and a couple of signal generators, if you play with one of those Lissajous patterns get their name from Jules Antoine Lissajous, who investigated, wrote and lectured about them in 1857. A Lissajous figure is produced by taking two sine waves and Software Terms: muellerr, Engineering, Programming, traveling, 3d scanner, van de graaff, pulse jet, Tetris Years ago people discovered that you can create nice shapes using the XY mode of oscilloscopes and function generators. Arregui Department of Electrical and Electronic Engineering, Public University of Navarra, Pamplona, Spain The device is small, cheap and easy to assemble. 7 are shown in Fig. And the picture indeed shows a distance of about 1. Add Lissajous Curve to your PopFlock. Thanks to the Lissajous curve we can immediately tell that the phase difference is 45 degrees. Generator 1 was set at 1 kHz. If the ratio of the frequencies is rational, the curve will always eventually close. Here's the setup, including the schematic for a very simple audio generator. LissajousGenerator (axes, units, centre, span, lobes, size=None, alternate=False) [source] ¶. We note that the 3-D Lissajous curve method proposed in Generate tons of puns! Be the wittiest tweeter, texter, and writer wherever you go! curves Software - Free Download curves - Top 4 Download - Top4Download. enough horsepower to run these low frequencies for lissajous figures. Some of these, the Epitrochoids and Epicycloids, may be familiar if you had a Spirograph as Experiment to investigate Lissajous figures. 3, pp. Lissajous curves are a special case of the harmonograph with damping constants . lissajous curve generator

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