Problem in X-Y Plot

#1 Pubblicato: 26/02/2025 19:30:34

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Hello all,

Again I recur to the Question Forums to attempt to solve an issue that I, single handely, cannot fix.
The issue I'm attempting to solve revolves around the definition of the movement of a certain bell, and the Horizontal forces produced by such movement.
In the attempt of solving this issue, I recurred to "Cephes Mathematical Library" Plugin, due to the necessity of implementing Jacobian Elipting Functions, as they are vital to obtain a more accturate discription of reality.
The problem I'm encountering is that the graph I create does not show anything at all, no matter how much I increase the frame window, or force parameters in the functions and equations I utilize.

I know this is quite the niche problem, but, if anyone has encountered similar problems as I have, I would be happy to hear solutions or steps to one.
I'll annex the SMath file for further investigation if necessary.

Much appreciated.
Frequency Analysis_v1.sm (15,7 KiB) scaricato 1860 volta(e).

#2 Pubblicato: 26/02/2025 20:24:08

StvMath

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The problem lies with the sine function. Your argument to the sine function has units. It needs to be unitless.

#3 Pubblicato: 26/02/2025 21:29:56

João Pereira

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Wrote
The problem lies with the sine function. Your argument to the sine function has units. It needs to be unitless.

Thank you very much for the assistance. I understanad what you're saying, but how do I resolve that issue? I'm kind of lost.

Thanks in advance for the assistance

#4 Pubblicato: 26/02/2025 23:31:36

StvMath

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Wrote

Wrote
The problem lies with the sine function. Your argument to the sine function has units. It needs to be unitless.

Thank you very much for the assistance. I understanad what you're saying, but how do I resolve that issue? I'm kind of lost.

Thanks in advance for the assistance

There seems to be an error in the expression for phi(t). However, I would need to see how it was derived to stand a chance of helping further.

#5 Pubblicato: 27/02/2025 11:57:44

Alvaro

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Olá João. Some notes in the attached file.

Frequency Analysis_v1.sm (154,3 KiB) scaricato 1876 volta(e).

Best regards.
Alvaro.

#6 Pubblicato: 27/02/2025 21:36:31

João Pereira

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Wrote

Wrote

Wrote
The problem lies with the sine function. Your argument to the sine function has units. It needs to be unitless.

Thank you very much for the assistance. I understanad what you're saying, but how do I resolve that issue? I'm kind of lost.

Thanks in advance for the assistance

There seems to be an error in the expression for phi(t). However, I would need to see how it was derived to stand a chance of helping further.

Hello again, I took the expression from the agllomerate of a couple of thesis work I discovered when studying the process. As the actual derrivation is quite complicated, but was common between papers, I didn't bother for it's confirmation.
Nevertheless, could you point me the error for the expression in phi(t)?

Thanks in advance.

#7 Pubblicato: 27/02/2025 21:40:50

João Pereira

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Olá João. Some notes in the attached file.

Frequency Analysis_v1.sm (154,3 KiB) scaricato 1876 volta(e).

Best regards.
Alvaro.

Alvaro, very much appreciate the efforts you placed in a project that doesn't affect you in any way, it is very much appreciated.
Nevertheless, I do have some questions behind some of the processes you did. Firstly, I believe you changed the sn( 1; 2) function I utilized to a simpler sin() function, I must ask if that was mostly due to simplification of the analytical processes or if there was any other reasoning behind it.
Secondly, you refer that phi(t)' and phi(t)'' have different units and, therefore, H(t) will be incorrect. How could one attempt to resolve that issue?

Thank you very much in advance.

#8 Pubblicato: 28/02/2025 02:06:25

Alvaro

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... Firstly, I believe you changed the sn( 1; 2) function I utilized to a simpler sin() function, I must ask if that was mostly due to simplification of the analytical processes or if there was any other reasoning behind it. ...

Because I don't know how to find the derivative of the arcsin of a complicated Jacobi elliptical si expression. Actually, Wolfram neither. In this version I restored the function sn and the derivatives are found numerically.

Wrote
... Secondly, you refer that phi(t)' and phi(t)'' have different units and, therefore, H(t) will be incorrect. How could one attempt to resolve that issue?

The way it is written, the units of H do not match. However, I do not know how to fix them because I have no idea what H could be. Is it the Hamiltonian? If you provide some theoretical framework, maybe I can understand a little better what you are trying to solve. Also, there are many unused variables: volume, thickness, beats per minute, diameter...

Numerical and symbolic solution, for what I suppose is the problem to be solved:

Frequency Analysis_v2.sm (189,94 KiB) scaricato 1840 volta(e).

Best regards.
Alvaro.

#9 Pubblicato: 28/02/2025 20:36:32

StvMath

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Wrote

Hello again, I took the expression from the agllomerate of a couple of thesis work I discovered when studying the process. As the actual derrivation is quite complicated, but was common between papers, I didn't bother for it's confirmation.
Nevertheless, could you point me the error for the expression in phi(t)?

Thanks in advance.

Can you upload (or provide a link to) the two papers you mention?

#10 Pubblicato: 01/03/2025 17:59:27

sergio

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A long time ago I addressed the problem by writing this scilab script that I am attaching, omitting only the part for the production of the graphs. It also works to date. Maybe it can be useful to you, at the moment I don't have time to try to transform it into something Smath
sergio

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Alvaro 02/03/2025 07:37:00

#11 Pubblicato: 02/03/2025 07:38:48

Alvaro

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A long time ago I addressed the problem by writing this scilab script ...

Hi Sergio. A solution, I guess that it is the same.

Campana di Pompelmo.pdf (524,95 KiB) scaricato 1024 volta(e).

Campana di Pompelmo.sm (1,01 MiB) scaricato 1822 volta(e).

Best regards.
Alvaro.

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sergio 02/03/2025 23:12:00

#12 Pubblicato: 02/03/2025 22:55:50

João Pereira

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To all the involved in the assistance of this work I thank you deeply, I would not discover the necessary means to solve the problem I was trying to solve without the assistance provided.

Cheers to all.
João

#13 Pubblicato: 02/03/2025 23:50:01

sergio

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Alvaro, first of all thanks for the great job. I found an important mistake (partly caused by my lightness in the use of the "K" variable). %K is a Scilab function for the calculation of the Jacobi's complete elliptic integral of the first kind (I hope Smath has this function available)

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sergio

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Alvaro 03/03/2025 01:28:00

#14 Pubblicato: 03/03/2025 01:25:43

Alvaro

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Hi Sergio. Don't worry. The procedure is robust, this is, accept that kind of variations.

Campana di Pompelmo v2.sm (1,01 MiB) scaricato 1870 volta(e).

Best regards.
Alvaro.

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sergio 03/03/2025 02:44:00

#15 Pubblicato: 03/03/2025 02:53:07

sergio

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Alvaro thanks again.
Only a annotation for the calculation of the "K" function: you gave two methods (indicating what you think preferable); The other method numerically provides the same value provided by Scilab and in fact two rather different periods of oscillation are obtained as indicated below (2.02 s against 2.27 s).
I have no mathematical knowledge so high to be able to evaluate this difference that does not seem to me to be of an exclusively numerical type.

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sergio

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Alvaro 03/03/2025 04:18:00

#16 Pubblicato: 03/03/2025 04:24:39

Alvaro

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Hi Sergio. You're right. I couldn't find the function among the plugins, so I looked for equivalent ways of writing it on the Wolfram functions site. However, numerical problems with a 4-variable function can be really serious. Surely there is some other, more accurate way, and one that doesn't involve using Maple just to evaluate a function, no matter how special it is.

https://functions.wolfram.com/EllipticIntegrals/EllipticK/26/01/01/