How can the shape in this picture be descibed mathematically?












1












$begingroup$


I'm reading an article on Boltzmann that contains the following figure:
enter image description here



It is obviously related to harmonic oscillators (since the article says so), but how could I describe this figure mathematically? I've seen it somewhere before, but have no recollection of where.






mathematical-physics mathematical-modeling







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  • 4




    $begingroup$
    en.wikipedia.org/wiki/Lissajous_curve
    $endgroup$
    – Lord Shark the Unknown
    Jan 4 at 19:20
















1












$begingroup$


I'm reading an article on Boltzmann that contains the following figure:
enter image description here



It is obviously related to harmonic oscillators (since the article says so), but how could I describe this figure mathematically? I've seen it somewhere before, but have no recollection of where.






mathematical-physics mathematical-modeling







share|cite|improve this question









$endgroup$








  • 4




    $begingroup$
    en.wikipedia.org/wiki/Lissajous_curve
    $endgroup$
    – Lord Shark the Unknown
    Jan 4 at 19:20














1












1








1





$begingroup$


I'm reading an article on Boltzmann that contains the following figure:
enter image description here



It is obviously related to harmonic oscillators (since the article says so), but how could I describe this figure mathematically? I've seen it somewhere before, but have no recollection of where.






mathematical-physics mathematical-modeling







share|cite|improve this question









$endgroup$




I'm reading an article on Boltzmann that contains the following figure:
enter image description here



It is obviously related to harmonic oscillators (since the article says so), but how could I describe this figure mathematically? I've seen it somewhere before, but have no recollection of where.






mathematical-physics mathematical-modeling




mathematical-physics mathematical-modeling






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 4 at 19:20









TheSodesaTheSodesa

1198




1198








  • 4




    $begingroup$
    en.wikipedia.org/wiki/Lissajous_curve
    $endgroup$
    – Lord Shark the Unknown
    Jan 4 at 19:20














  • 4




    $begingroup$
    en.wikipedia.org/wiki/Lissajous_curve
    $endgroup$
    – Lord Shark the Unknown
    Jan 4 at 19:20








4




4




$begingroup$
en.wikipedia.org/wiki/Lissajous_curve
$endgroup$
– Lord Shark the Unknown
Jan 4 at 19:20




$begingroup$
en.wikipedia.org/wiki/Lissajous_curve
$endgroup$
– Lord Shark the Unknown
Jan 4 at 19:20










1 Answer
1






active

oldest

votes


















2












$begingroup$

Lissajous figure with $x = sin (4 t)$ and $y = sin (7 t)$.



Count the number of extrema along the top and along the side to get the ratio of frequencies.



enter image description here






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
    $endgroup$
    – marty cohen
    Jan 4 at 20:32











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1 Answer
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1 Answer
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active

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active

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2












$begingroup$

Lissajous figure with $x = sin (4 t)$ and $y = sin (7 t)$.



Count the number of extrema along the top and along the side to get the ratio of frequencies.



enter image description here






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
    $endgroup$
    – marty cohen
    Jan 4 at 20:32
















2












$begingroup$

Lissajous figure with $x = sin (4 t)$ and $y = sin (7 t)$.



Count the number of extrema along the top and along the side to get the ratio of frequencies.



enter image description here






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
    $endgroup$
    – marty cohen
    Jan 4 at 20:32














2












2








2





$begingroup$

Lissajous figure with $x = sin (4 t)$ and $y = sin (7 t)$.



Count the number of extrema along the top and along the side to get the ratio of frequencies.



enter image description here






share|cite|improve this answer











$endgroup$



Lissajous figure with $x = sin (4 t)$ and $y = sin (7 t)$.



Count the number of extrema along the top and along the side to get the ratio of frequencies.



enter image description here







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Jan 4 at 20:47

























answered Jan 4 at 19:55









David G. StorkDavid G. Stork

10.6k31332




10.6k31332












  • $begingroup$
    Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
    $endgroup$
    – marty cohen
    Jan 4 at 20:32


















  • $begingroup$
    Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
    $endgroup$
    – marty cohen
    Jan 4 at 20:32
















$begingroup$
Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
$endgroup$
– marty cohen
Jan 4 at 20:32




$begingroup$
Just get out your oscilloscope and a couple of sine wave generators. (From my high school physics lab)
$endgroup$
– marty cohen
Jan 4 at 20:32


















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