Geometrical and graphical representations analysis of lissajous. Lissajous figure on an oscilloscope, displaying a 3. However, if the periods are related as integers, the moving point will return to its original position in a period of time equal to the least multiple of the two periods, and a lissajous figure with a more complex shape is produced. Pdf calibrating the frequency of tuning forks by means of. Lissajouslike figures with triangular and square waves scielo. Measurement of the speed of sound in air medium using. Lissajous figures where a 1, b n n is a natural number and. Pdf calibrating the frequency of tuning forks by means.
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. In most oscilloscopes that have this capability, the frequency domain is accessed by pressing a button labeled math. Lissajous work in the nineteenth century centered around the study of vibrating objects and wave phenomena. Circuits and electronics laboratory a lissajous leesuhzhoo.
The resulting pattern was a function of theratio of the two frequencies. Lissajous figures, triangular and square waves, fourier analysis. Lissajous figure definition is any of an infinite variety of curves formed by combining two mutually perpendicular simple harmonic motions, commonly exhibited by the oscilloscope, and used in studying frequency, amplitude, and phase relations of harmonic variables. Lissajous patterns lissajous figures or lissajous curve. When the phase shift is 45, the lissajous pattern is an ellipse whose centerline slopes upward from left to. To use this catalogue, adjust the oscilloscope so that the x and y. If the two waves do not start at the same instant we get different patterns for the same frequency ratio. Lissajous patterns of cro or cathode ray oscilloscope. One example 0 12 1 11 10 2 6 7 5 9 3 8 4 the diagram shown is identical to one of the figures you can obtain with the laser. The setup in the picture consists of two pendulums constrained to move perpendicular to each other. The lissajous lab provides you with a virtual oscilloscope which you can use to generate these patterns.
This property is exploited to produce a set of points, called padua points, at which a function may be sampled in order to compute either a bivariate interpolation or quadrature of the function over the domain. Lissajous attached mirrors to the two forks, which were positioned orthogonally, and shone a beam of light on a screen, via the two mirrors see illustration. Which makes these lissajous patterns very useful to analysis the signals applied to deflection plated of cro. Lissajous figures where a 1, b n n is a natural number and 2 1 s g n n 3 lissajous curves can also be generated using an oscilloscope as illustrated. This is an article about lissajous curves 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.
Lissajous pattern theory lissajous figure or lissajous pattern is the quickest way to calculate frequency and phase difference. 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 lissajous curves. Lissajous figures are patterns generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another. Dec 12, 2012 the resulting pattern was a function of theratio of the two frequencies.
A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous figures a lissajous figure is produced by taking two sine waves and displaying them at rightangles to each other. Lissajous figures are not observed if the periods differ substantially. We have to do work on multitasking to overcome this problem. Dec 27, 2012 lissajous pattern theory lissajous figure or lissajous pattern is the quickest way to calculate frequency and phase difference.
The patterns that appear at the cro screen on connecting both pairs of the deflection plates horizontal deflection plates and vertical deflection. Lissajous art creatorplayground only works in browsers that support the html5 canvas tag. How to draw 2d oscillations and lissajous curves using 3d. Trigonometryfor enthusiastslissajous figures wikibooks. On the screen, the vibrations of the two mirrors are translated into the horizontal and vertical motion of the point of light, and a closed elliptical pattern results if the frequencies of. Aug 07, 2018 shape of these lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection plates traces of cro.
Replacing the cosine function in the parametrization by a triangle wave transforms every lissajous knot isotopically into a billiard curve inside a cube. Lissajous pattern obtain in labview having frequency ratio 2. Or it can be used to create and save your own lissajous artwork. The theory of discrete lissajous figures is developed. Sep 29, 2018 lissajous patterns are the plane curves traced by a point that executes two independent harmonic motions in perpendicular directions. A variation is the display of signals in the frequency domain. In knot theory, a lissajous knot is a knot defined by parametric. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on youtube. Lissajous figures article about lissajous figures by the. When the phase shift is 90 or 270, and both signals are the same frequency, a perfect circle displays. The pattern of crisscross lines is actually a lissajous figure. Lissajous figure, also called bowditch curve, pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. The applet also allows you to apply a signal to modulate the hue of the trace, so you can create colorful designs.
The horizontal axis displays the signal input to a loudspeaker while the vertical axis displays the changing signal picked up by a microphone as it is moved to a known distance away from the source. A labview based simulation of lissajous pattern using daq card. The most common use of an oscilloscope is to display one or more signals in the time domain. Aug 11, 2016 the same lissajous pattern is displayed when the phase shift is 360, illustrating that these two phase shifts are equivalent. Jules antoine lissajous 18221880 was a french physicist who was interested in waves, and around 1855. Meanwhile, the theory of lissajous figures827 finds a wide range of applications in engineering 9,28physics10,11and biomedicince12. These lissajous patterns have two applications to analysis the signals. Geometrical and graphical representations analysis of. Shape of these lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection plates traces of cro. The relation between the discrete lissajous figures. This video takes a fairly detailed look at the basics of lissajous patterns on an oscilloscope.
Named after jules antoine lissajous, a lissajous curve. Determine the inductance of the coil by i fitting the theoretical. Lissajous patterns at the dawn of the technological revolution. Rc, rl and rlc series circuits as a function of frequency f. Jan 12, 2015 this is a project work on electrical representation on lissajous figure. The lissajous patterns for other frequency ratios can be similarly drawn. The frequencies of the motion are in the ratio of two integers. To use lissajous figures to take phase measurements theory lissajous patterns are. Calibrating the frequency of tuning forks by means of lissajous figures article pdf available in american journal of physics 795. A lissajous curve, named after jules antoine lissajous is a. He would use sounds of different frequencies to vibrate a mirror 5.
Lissajous patterns of cro or cathode ray oscilloscope electrical4u. Lissajous patterns experiment 3 linkedin slideshare. Lissajous pattern may be constructed in the usual way and a 8 shaped pattern with two loops is obtained. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The figures, sometimes called bowditch curves, were first described in the early 1800s by american mathematician nathaniel bowditch, who experimented with a pendulum undulating around perpendicular axes at the same time. Shape of these lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection. In mathematical29terminology, a lissajous curve is a. Lissajous figures displayed on an oscilloscope can be used to give a quick estimate of the relative. Lissajous figure definition of lissajous figure by merriam. Lissajous figure is a subject too wideranging to allow a comprehensive coverage of all of the.
Lissajous pronounced leesuhzhoo figures were discovered by the french physicist jules antoine lissajous. We show a generalization of the wellknown lissajous figures, changing the two orthogonal. This page can be used as a playground or learning tool to see how changing basic parameters affects the generated images. Lissajous figure definition and meaning collins english. If the oscilloscope hasthe xversusy capability, one can apply one signal to the vertical deflection. Pdf discrete lissajous figures and applications researchgate. Lissajous patterns at the dawn of the technological revolution the lissajous pattern or lissajous figure is named for the french mathematician jules antoine lissajous 1. First studied by the american mathematician nathaniel bowditch in 1815, the curves were investigated independently by the french mathematician julesantoine lissajous in 185758. Lissajous curves can also be generated using an oscilloscope. Frequency measurement by lissajous method basic circuit. Basics of lissajous patterns on an oscilloscope youtube. Some of these patterns are shown in the below figure.
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