Hi there, this is a tutorial explaining the construction of a very basic Lissajous emulator in Excel.

It’s supposed to be very easy to understand at the high school level.

Good luck,

George

## A Lissajous emulator in Excel

by George Lungu

### Introduction:

Jules A. Lissajous was a French mathematician from the 19th century

– He wanted to visualize waves.

– He started by using tuning forks resonating in the water in order to create standing waves.

– Eventually he settled for bouncing a beam of light off two small mirrors each connected to a different tuning fork. After that, the beam was projected on a wall.

– Nowadays the Lissajous figures are commonly generated using oscilloscopes by driving both the X and Y axes with sinusoidal signals.

– An example of an application is measuring the phase difference between two signals.

– Below is a series of Lissajous figures from Wikipedia for sinusoidal signals having the follo-wing ratios of frequencies: 1:2, 3:2, 3:4, 5:4, 5:6, 9:8 and a difference in phase of pi/4.

### Implementation – How is this done in Excel?

#### -The two waves are expressed as:

A = sin(2pn1t+f1)

B = sin(2pn2t)

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The time column (column “A”):

• A16 = 0

• A17 = A16+B$13

• Copy down A17 to A18, A19,…., A700

X column (column “B”) – first wave:

• B16 = SIN(RADIANS(2*PI()*B$3*A16+B$7))

• Copy down B16 to B17, B18, …., B700

Y column (column “C”) – second wave:

• C16 = SIN(RADIANS(2*PI()*B$5*A16))

• Copy down C16 to C17, C18, …., C700

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#### Let’s chart the following data on a 2D scatter plot:

X as B16:B700

Y as C16:C700

#### Create three macros for controlling the frequencies and difference in phase between the two waves:

Private Sub Frequency_1_Change()

Range(“B3”) = Frequency_1.Value / 10

End Sub

Private Sub Frequency_2_Change()

Range(“B5”) = Frequency_2.Value / 10

End Sub

Private Sub Phase_1_Change()

Range(“B7”) = Phase_1.Value

End Sub

5

A Few Screenshots:

– 1.5 -1 -0.5 0 0.5 1 1.5

0

– 1.5 -1 -0.5 0 0.5 1 1.5

0

– 1.5 -1 -0.5 0 0.5 1 1.5

by George Lungu <www.excelunusual.com>

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