Solve Lissajou's Figure Problem with 1:2 Frequency Ratio

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The discussion revolves around solving a Lissajou's figure problem with a frequency ratio of 1:2, where the phase difference is unspecified. Participants note that this could lead to either a parabola or a figure-eight shape, creating confusion since both options are presented. Clarification is sought regarding the orientation of the figure-eight, with suggestions that it may need to be aligned in a specific way. Ultimately, the consensus leans towards the figure-eight being the correct representation rather than the parabola. The conversation emphasizes the importance of understanding phase differences in determining the correct Lissajou's figure.
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Homework Statement



The problem in which I have difficulty has been posted as an attachment. It is based on Lissajou's figure. In the given problem, the ratio of the frequency is 1:2 but nothing has been mentioned about the phase difference. As far as my knowledge goes, the corresponding Lissajou's figure can either be a parabola or a figure of eight. The difficulty that I am facing is that, both the options are given. Is there any additional information that I have failed to notice in the question? Any help is most welcome.


Homework Equations




The Attempt at a Solution

 

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Amith2006 said:

Homework Statement



The problem in which I have difficulty has been posted as an attachment. It is based on Lissajou's figure. In the given problem, the ratio of the frequency is 1:2 but nothing has been mentioned about the phase difference. As far as my knowledge goes, the corresponding Lissajou's figure can either be a parabola or a figure of eight. The difficulty that I am facing is that, both the options are given. Is there any additional information that I have failed to notice in the question? Any help is most welcome.


Homework Equations




The Attempt at a Solution


If it were a figure 8, which way would the figure 8 be oriented?
 
As I read the question, three could be more than 1 correct option, but take good look
at that figure 8.
 
Do u mean that the figure 8 should have been aligned in the horizontal plane? Hence the more appropriate answer is the parabola. Am I heading in the right direction now?
 
Amith2006 said:
Do u mean that the figure 8 should have been aligned in the horizontal plane? Hence the more appropriate answer is the parabola. Am I heading in the right direction now?

It's not a parabola, but about the figure 8, yes.
 

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