: PROJECT WORK FOR PH2101:

NAME OF THE PROJECT: ELECTRICAL REPRESENTATION OF

LISSAJOUS FIGURE

NAME OF THE GROUP MEMBERS:

1. SUSHOVAN MONDAL (13MS050)

2. SUMAN DAS (13MS019)

3. MANOJ KUMAR (13MS099)

4. SANTOSH KUMAR (13MS033)

GUIDED BY: Dr. BIPUL PAL

OBJECTIVES:

1. Use Lissajous figure to determine frequency of an unknown

sinusoidal curve.

NECESSARY EQUIPMENTS:

1. Cathode Ray oscilloscope (CRO)

2. Function Generator.

THEORY:

Lissajous figures are actually a figure of superposition of two

perpendicular waves. When two perpendicular sinusoidal waves with two

different frequencies (one should be the rational multiple of other) are

superposed then various types of closed patterns are formed. Depending on

the frequencies applied and changing the relative phase between them we can

obtain various types of Lissajous figure. And by analyse these patterns we can

calculate the phase difference and frequency of an unknown sinusoidal curve.

Here we are using A.C signals as sinusoidal wave of various frequencies and

phase and monitor the resultant shape on the screen of CRO.

This type of technic (Obtain the Lissajous figure) was used in early

days to know the frequency of sinusoidal curves. The closed figures are mainly

3 types like 1. Straight line (When phase difference is zero or pi). 2. Circle

(When amplitude of both signals are same and phase difference is pi/2)

3.Ellipse (Various types of ellipse can be formed by changing frequencies in

various orientation.).

MATHEMATICAL EXPRESSION AND REQUIRED FORMULAES:

Say two sinusoidal waves are superposed perpendicularly are given by

and . Where and are angular

frequencies of two sinusoids and their relative phase difference is . So now

we can write,

(

) , √

*√

*

( (

) ) *√

*

)

So from this equation we can obtain various types of figures by changing the

values of .This equation is obtained for only when the frequency ratio is 2

.we can obtain various types of figures by changing the frequency ratio also.

FREQUENCY DETERMINATION BY LISSAJOUS FIGURE:

1. Two obtain Lissajous figure we need two function generator and a CRO.

2. At first we put an A.C signal to obtain the sinusoidal pattern and after

that we do the same thing for another one.

3. Then we fix the frequency of one generator (5 KHz) .

4. Then we put the CRO in XY mode to superpose the waves

perpendicularly.

5. Then we vary the frequency and check where we get the closed loop like

Lissajous figure.

6. Then we capture the figure and draw two tangents along X axis and Y

axis such that lines just touch the peak point of the curve.

7. And the numbers of the touching points of points that is touched by the

tangents in each side are counted.

8. And their ratio is the ratio between two frequencies of those sinusoids.

9. One of the frequency is already known, and we calculate other

frequencies.

RESULTS AND ANALYSIS OF THE OBTAINED LISSAJOUS FIGURE:

Number of horizontal tangencies =1, No. of vertical tangencies = 1.

Applied frequency of the wave in Y direction = 5 KHz.

So, Applied frequency of the wave in X direction = 5 KHz.

Number of vertical tangencies = 1

Number of horizontal tangencies =2

Applied frequency of the wave in Y direction = 5 KHz

Applied frequency of the wave in X direction = 10 KHz

Number of vertical tangencies = 1

Number of horizontal tangencies =3

Applied frequency of the wave in Y direction = 5 KHz

Applied frequency of the wave in X direction = 15 KHz

Number of vertical tangencies = 1

Number of horizontal tangencies =5

Applied frequency of the wave in Y direction = 5 KHz

Applied frequency of the wave in X direction = 25 KHz

Number of vertical tangencies = 1

Number of horizontal tangencies =4

Applied frequency of the wave in Y direction = 5 KHz

Applied frequency of the wave in X direction = 20 KHz

This is also representation of linear Lissajous figure, which is obtained by

superposition of two perpendicular sin waves with equal frequency with phse

difference pi/4.

DISCUSSION:

In our experiment we just want to show the Lissajous pattern and from

the obtained figure we want to determine an unknown wave frequency. The

experiment is quite good if we use two coherence sources and to get such type

of source we have to use same source of wave. But we use two different wave

generators and for this cause obtained Lissajous figure on CRO is not stable.

But if use same source then we cannot vary frequency in two different ways.

But by taking the screen shot of the moving Lissajous figure we can analyse the

figure and determine the frequency of an unknown wave perfectly.

Other than our experiment we can also calculate phase difference of two

waves from the Lissajous figure. Then those figures are mainly elliptical in

various directions and circular and linear patterns. But there is no phase

regulator with the function generator so we cannot obtain these types of

figures.

So other than these types of errors we get very good result to determine

the frequency of an unknown wave.

CONCLUSION:

We have tried as much as possible to get lissajous pattern to calculate

various frequencies. But due to some technical problem we did not get the

exact pattern in all the cases. But overall we are quite satisfied by doing this

type of enjoyable experiment.

ACKNOWLEDGEMENT:

We want to convey heartily thanks to Dr. Bipul Pal to guide our

experiment and also Gour Da and Rajani madam to help us during our

experiment. And thanks to every body of physics lab to support us in our

experiment.

REFERENCE:

1. N.K Bajaj

2. www.google.com