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Physics-

General

Easy

Question

Lissajous figure shown in figure. Corresponds to which one of the following

Phase difference $π / 2$ and period 1 : 2
Phase difference $3 π / 4$ and period 1 : 2
Phase difference $π / 4$ and period 2 : 1
Phase difference $2 π / 3$ and period 2 : 1

The correct answer is: Phase difference $pi divided by 2$ and period 1 : 2

The Lissajous figure will be parabola if period ratio is $1 colon 2$ and phase difference is $pi divided by 2$
Let $x equals a sin invisible function application left parenthesis 2 omega t plus pi divided by 2 right parenthesis a n d blank y equals b sin invisible function application omega t$
$therefore blank sin invisible function application omega t equals y divided by b$
Now, $fraction numerator x over denominator a end fraction equals sin invisible function application left parenthesis 2 omega t plus pi divided by 2 right parenthesis equals cos invisible function application 2 omega divided by t$
$equals 1 minus 2 sin to the power of 2 end exponent invisible function application omega t equals 1 minus fraction numerator 2 y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction$
or $fraction numerator 2 y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 minus fraction numerator x over denominator a end fraction equals negative open parentheses fraction numerator x minus a over denominator a end fraction close parentheses$
or $y to the power of 2 end exponent equals negative fraction numerator b to the power of 2 end exponent over denominator 2 a end fraction left parenthesis x minus a right parenthesis$
it is an equation of a parabola as given in figure

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