Functional representation of the oscillating graph

[yilmaz]

Homework Statement

this is actually not a homework

Relevant Equations

tsin(ct)

Hi;

This is in fact not a homework question, but it rather comes out of personal curiosity.
If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?

 

[berkeman]

Welcome to PF.

Can you tell us more about where you got these plots? What do they represent? Can you give a link to the website or paper where you found them? Thanks.

 

[haruspex]

They look like $x \sin(\omega x)$, which I see you have indicated already. What is wrong with that?

 

[yilmaz]

They look like $x \sin(\omega x)$, which I see you have indicated already. What is wrong with that?

Hi @haruspex,

It actually works, but only for positive x. For negative x, I want to see it mirrored, and in addition I would like to avoid using abs or conditionals in the function.

 

[yilmaz]

Welcome to PF.

Can you tell us more about where you got these plots? What do they represent? Can you give a link to the website or paper where you found them? Thanks.

hi berkeman,

It’s actually my plot, so there’s no link. It’s the result of an evolutionary algorithm for a specific problem , where I consistently get such graphs. Since I’m not a physicist, I wanted to consult if there is any simple function representation that fits the shape.

 

[vela]

How about $x^2 \sin x$?

 

[berkeman]

It’s actually my plot, so there’s no link. It’s the result of an evolutionary algorithm for a specific problem , where I consistently get such graphs.

What is the difference between the two plots? Did you just squeeze the horizontal axis to make the 2nd plot?

Also, it looks a lot like an AM modulated sine wave to me...

https://ccrma.stanford.edu/~jos/rbeats/img34.png

 

[haruspex]

How about $x^2 \sin x$?

Good point.. it is not $x \sin (x)$ since that is an even function whereas the graphs show an odd function. But whether the peaks show a quadratic behaviour is unclear. Could be something like $x^{\frac 23} \sin (x)$

 

[yilmaz]

How about $x^2 \sin x$?

Thanks @vela, that’s pretty close but when plotted, it doesn’t cut the origin like a diagonal as in the two sample graphs, but rather becomes tangent. But that’s a nice clue.

 

[vela]

You want an odd function, so try $x \cos x$.

 

[yilmaz]

You want an odd function, so try $x \cos x$.

great, I think this really looks the same! thanks a lot!

 

[haruspex]

Thanks @vela, that’s pretty close but when plotted, it doesn’t cut the origin like a diagonal as in the two sample graphs, but rather becomes tangent. But that’s a nice clue.

Do you have the curves as datapoints? If you figure out the frequency (looks sort of constant) you could divide by $\sin(\omega x)$ and try to fit the resulting curve.

 

[yilmaz]

What is the difference between the two plots? Did you just squeeze the horizontal axis to make the 2nd plot?

Also, it looks a lot like an AM modulated sine wave to me...

View attachment 315930
https://ccrma.stanford.edu/~jos/rbeats/img34.png

thanks @betk

Do you have the curves as datapoints? If you figure out the frequency (looks sort of constant) you could divide by $\sin(\omega x)$ and try to fit the resulting curve.

yes i have the datapoints, I’ll try to figure out then…

 

[yilmaz]

What is the difference between the two plots? Did you just squeeze the horizontal axis to make the 2nd plot?

Also, it looks a lot like an AM modulated sine wave to me...

View attachment 315930
https://ccrma.stanford.edu/~jos/rbeats/img34.png

the difference of the two plots are coming from two different random runs.

 

[berkeman]

the difference of the two plots are coming from two different random runs.

Why the big difference in spatial frequency? What are the units for your two axes?

 

[yilmaz]

Why the big difference in spatial frequency? What are the units for your two axes?

Actually since the x-axis (the domain of the function) is also subject to evolution, the result may come in different shapes. But you can take only one of them as reference. However, as @vela stated, xcos(x) works quite well, I guess this is the function that I was looking for.