Lissajous Figures

• Drag to change the angle of viewing.
• 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.
• Deflection plate is red (black) when it is positive (negative).
• The screen is viewed directly from the front when the box "Front" is checked. Click a point on the screen will show the coordinates of that point.
• The Lissajous figures shown elsewhere may look different to those generated here (by specifying the same frequency ratio and initial phases). Most probably they use a different mathematical form of the signals, e.g., the cosine function.

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 Html5 Version(Generalized Lissajous Figures)

### (I) Finding frequency ratio and phase difference (φ) from Lissajous figures

#### (a) 0o, 90o, 180o

(Amp = Amplitude; assume same voltage sensitivity)

φ = 0o

φ = 180o

φ = 90o
(Ampx = Ampy)

φ = 90o
(Ampx > Ampy)

φ = 90o
(Ampx < Ampy)

#### (b) General Case

We do not known whether x leads y or y leads x unless the sense of rotation is known.

### (II) Frequencies are different, but in a simple ratio

The pattern generally depends on x- and y-frequency and their initial phases. The ratio of the two frequencies can be found easily by the following method:

Draw a vertical and a horizontal line to cut the pattern curve, but avoid passing through any self-intersection points of the pattern curve.

Count the number of intersection points of the vertical line with the pattern curve. Let this number be m.

As well,

count the number of intersection points of the horizontal line with the pattern curve. Let this number be n.

Hence, x-frequency : y-frequency = m : n.
In this example, the ratio is 6 : 4 = 3 : 2.

One more example,

x-frequency : y-frequency = 2 : 3

 Author and Copyright: Chiu-king Ng Feedback/Contact: feedbackXY@phy.hk, where XY is the prime number following 23 Mirror Site: http://phy.hk Last Update: 31-5-2017