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Lissajous Figures Oscilloscope Pdf Download ->->->-> http://shurll.com/a3ewo
Application.for.the.case.of.a.=.b[edit]Prior.to.modern.computer.graphics,.Lissajous.curves.were.typically.generated.using.an.oscilloscope.(as.illustrated)Very..different..curves..may..arise..from..the..same..value..of..a/b..but..different..values..of..are..Chebyshev..polynomials..of..the..first..kind..of..degree..Na..=..1..,..b..=..1..,..A..=..1..,..B..=..1..{displaystyle..displaystyle..a=1,b=1,A=1,B=1}..and..δ..=..π../..2..{displaystyle..displaystyle..delta..=pi../2}..The..eccentricity..of..the..resulting..ellipse..is..a..function..of..the..phase..shift..between..the..input..and..output,..with..an..eccentricity..of..1..corresponding..to..a..phase..shift..of....90..∘..{displaystyle..pm..90^{circ..}}..and..an..eccentricity..of..∞..{displaystyle..infty..}..corresponding..to..a..phase..shift..of..0..or..180..degreesThe.appearance.of.the.figure.is.highly.sensitive.to.the.ratio.a/b.
News..&..EventsNewsFeature..StoriesEventsMedia..ResourcesOther.ratios.produce.more.complicated.curves,.which.are.closed.only.if.a/b.is.rationalMagnet...DevelopmentMagnet...Science...&...TechnologyApplied...Superconductivity...CenterFSU...Magnet...Research...&...Development,...IncYou.weLissajous...Curve[edit]Check..this..Try..the..lines..out..for..yourself
Another.simple.Lissajous.figure.is.the.parabola.(a/b.=.2,..=./2)For.a.ratio.of.1,.the.figure.is.an.ellipse,.with.special.cases.including.circles.(A.=.B,..=./2.radians).and.lines.(.=.0)Substitute..those..values..in..the..equation..and..simplifyUser..FacilitiesDC..FieldElectron..Magnetic..ResonanceHigh..B/TIon..Cyclotron..ResonanceNuclear..Magnetic..Resonance..&..Magnetic..Resonance..Imaging../..SpectroscopyPulsed..FieldMagnet..SearchThis...family...of...curves...was...investigated...by...Nathaniel...Bowditch...in...1815,...and...later...in...more...detail...by...Jules...Antoine...Lissajous...in...1857Check.this.Don't.just.take.our.word.for.it.that.the.Lissajous.equation.is.a.generalisation.of.the.equation.for.a.circle
The.figure.below.summarizes.how.the.Lissajous.figure.changes.over.different.phase.shiftswith.chosen.values.of.a.,.b.,.A.,.B.{displaystyle.displaystyle.a,b,A,B}.and.δ.{displaystyle.displaystyle.delta.}.and.with.t.{displaystyle.displaystyle.t}.varyingContents.1.Lissajous.Curve.2.Examples.3.Generation.4.Application.for.the.case.of.a.=.b.5.Notes.Lissajous...figures...were...first...mentioned...by...Nathaniel...Bowditch...in...1815,...and...rediscovered...by...Jules...Antoine...Lissajous...in...1857Lissajous..figure..on..an..oscilloscope.. bcfaf6891f
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