Lissajous-like figures with triangular and square waves

We show a generalization of the well-known Lissajous figures, changing the two orthogonal simple harmonic oscillations to triangular and square-wave-type oscillations. All figures cross the origin of axes when there is no phase difference between the oscillations. Aside from this common feature, squ...

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Bibliographic Details
Main Authors:	J. Flemming, A. Hornes
Format:	Article
Language:	Portuguese
Published:	Sociedade Brasileira de Física
Series:	Revista Brasileira de Ensino de Física
Subjects:	Lissajous figures triangular and square waves Fourier analysis
Online Access:	http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300031&lng=en&tlng=en

id	doaj-987e5362efde4245bdc1ba4cfc8f5031
record_format	Article
spelling	doaj-987e5362efde4245bdc1ba4cfc8f50312020-11-24T21:19:27ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-912635310.1590/S1806-11172013000300031S1806-11172013000300031Lissajous-like figures with triangular and square wavesJ. Flemming0A. Hornes1Universidade Estadual de Ponta GrossaUniversidade Estadual de Ponta GrossaWe show a generalization of the well-known Lissajous figures, changing the two orthogonal simple harmonic oscillations to triangular and square-wave-type oscillations. All figures cross the origin of axes when there is no phase difference between the oscillations. Aside from this common feature, square-wave-type figures show a very different behavior, with discontinuous phase changes and impossibility of using a simple formula to get the frequency ratio between the two component oscillations.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300031&lng=en&tlng=enLissajous figurestriangular and square wavesFourier analysis
collection	DOAJ
language	Portuguese
format	Article
sources	DOAJ
author	J. Flemming A. Hornes
spellingShingle	J. Flemming A. Hornes Lissajous-like figures with triangular and square waves Revista Brasileira de Ensino de Física Lissajous figures triangular and square waves Fourier analysis
author_facet	J. Flemming A. Hornes
author_sort	J. Flemming
title	Lissajous-like figures with triangular and square waves
title_short	Lissajous-like figures with triangular and square waves
title_full	Lissajous-like figures with triangular and square waves
title_fullStr	Lissajous-like figures with triangular and square waves
title_full_unstemmed	Lissajous-like figures with triangular and square waves
title_sort	lissajous-like figures with triangular and square waves
publisher	Sociedade Brasileira de Física
series	Revista Brasileira de Ensino de Física
issn	1806-9126
description	We show a generalization of the well-known Lissajous figures, changing the two orthogonal simple harmonic oscillations to triangular and square-wave-type oscillations. All figures cross the origin of axes when there is no phase difference between the oscillations. Aside from this common feature, square-wave-type figures show a very different behavior, with discontinuous phase changes and impossibility of using a simple formula to get the frequency ratio between the two component oscillations.
topic	Lissajous figures triangular and square waves Fourier analysis
url	http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300031&lng=en&tlng=en
work_keys_str_mv	AT jflemming lissajouslikefigureswithtriangularandsquarewaves AT ahornes lissajouslikefigureswithtriangularandsquarewaves
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Lissajous-like figures with triangular and square waves

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