solving simultaneous equations with Solve

#1 Pubblicato: 05/04/2022 15:45:27

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hi,
I used the Solve function a lot before but for some reason it does not work for this simple example.
I need to get the RayLeigh Damping factors alpha and beta using two frequencies, so two simple simultaneous equations should do it. tried using Solve but no luck.
Does anyone know why it is not solving?

Thanks in advance

File non trovato.File non trovato.

#2 Pubblicato: 05/04/2022 16:39:40

sergio

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Mostra spoiler

test_sergio.sm (8,05 KiB) scaricato 1248 volta(e).
sergio

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Mo 05/04/2022 22:22:00

#3 Pubblicato: 05/04/2022 18:24:50

overlord

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You can use roots() for your function. And a vectorize() can simplify it.
However, to use Assign() you will need this function to merge vars and solutions.

Regards

Assign_without_Maxima Solve().sm (7,36 KiB) scaricato 1319 volta(e).

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Mo 05/04/2022 22:22:00

#4 Pubblicato: 05/04/2022 22:22:48

Mo

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Thanks Overlord, PompelmoTell, greatly appreciated!!

#5 Pubblicato: 06/04/2022 10:28:07

⚜ Kenny Lemens, P.E. ᵂᴵ

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Greetings,

Another approach would be to use some elbow grease, you can substitute terms by hand and solve for 𝛼 and 𝛽:

Keypress (You can copy/paste the following into your worksheet):

α:{2*D*ω.1*ω.2}/{ω.1+ω.2}
β:α/{ω.1*ω.2}

*NOTE: ω.1 and ω.2 shown above are variables with subscript, they are not vectors ω[1 and ω[2; You should be able to substitute ω.1 for ω[1 if that serves your purposes.

- - -

- Kenny Lemens, P.E.

"No matter where you go, there you are." -Buckaroo BanzaiHotkeys: https://en.smath.com/forum/resource.ashx?a=45771&b=2

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Mo 06/04/2022 11:57:00

#6 Pubblicato: 06/04/2022 11:40:36

Fridel Selitsky

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If the damping coefficients are denoted by α1 and α2, you can use the function al_nlegsoive
test.sm (6,99 KiB) scaricato 1334 volta(e).

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sergio 06/04/2022 12:26:00, Mo 06/04/2022 11:57:00

#7 Pubblicato: 07/04/2022 11:08:53

Jean Giraud

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...

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Fridel Selitsky 07/04/2022 11:54:00

#8 Pubblicato: 07/04/2022 13:43:03

Jean Giraud

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... more in there from native Smath code.

Solve FindRoot FORUM.sm (10,9 KiB) scaricato 1304 volta(e).

#9 Pubblicato: 07/04/2022 17:27:55

overlord

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solving with uni's latest addition mathcad blocks;
you wouldn't need Eq: actually, but it can be shown.

mathblock.sm (5,15 KiB) scaricato 1307 volta(e).

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Mo 09/04/2022 22:28:00

#10 Pubblicato: 07/04/2022 18:19:34

overlord

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I think this is the most sophisticated method of my way.
It can get unknowns from equation, solve them.
In the end assigns numerical values to unknowns.
You don't need to define alpha or beta or any variable.
All process is automatic.

Regards

mathblock_v2.sm (5,19 KiB) scaricato 1323 volta(e).

There is also this way for guess define.

#11 Pubblicato: 08/04/2022 02:19:42

Fridel Selitsky

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Wrote
I think this is the most sophisticated method of my way.
It can get unknowns from equation, solve them.
In the end assigns numerical values to unknowns.
You don't need to define alpha or beta or any variable.
All process is automatic.

Regards
There is also this way for guess define.

This is good, but for a system of linear equations(our case), the guess can be arbitrary.

#12 Pubblicato: 08/04/2022 20:04:07

Martin Kraska

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And finally a version with Solve() and list injection region:

mathblock_Solve.sm (4,86 KiB) scaricato 1281 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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sergio 09/04/2022 04:48:00

#13 Pubblicato: 11/04/2022 09:57:44

⚜ Kenny Lemens, P.E. ᵂᴵ

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Greetings,

If plugins are considered, you can also consider the use of Maple:
- - -

In the image I posted, the 'equal sign' shown on those two equations are actually symbolic equals; keypress: [ctrl] + [.] instead of keypress [=].

Kenny Lemens, P.E.

"No matter where you go, there you are." -Buckaroo BanzaiHotkeys: https://en.smath.com/forum/resource.ashx?a=45771&b=2

#14 Pubblicato: 11/04/2022 16:44:08

Alvaro

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Hi. The isol solution, using only the Mathcad block plugin.

isol_example.sm (68,13 KiB) scaricato 1262 volta(e).
isol_example.pdf (34,57 KiB) scaricato 735 volta(e).

Best regards.
Alvaro.

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sergio 12/04/2022 05:01:00

#15 Pubblicato: 14/04/2022 12:10:17

Mo

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Thank you all for the feedback, is there a literature or manual to explain the Mathcad block plugin?
Thanks

#16 Pubblicato: 14/04/2022 14:54:00

Jean Giraud

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Wrote
Thank you all for the feedback, is there a literature or manual to explain the Mathcad block plugin ?

For that particular example, maple is an algebraic export.
Mathcad block has not yet been exemplified in Smath Community
of what it can do vs what native Smath can't.
Cheers ... Jean.

Codes Solve.sm (12,46 KiB) scaricato 1303 volta(e).

#17 Pubblicato: 14/04/2022 19:43:45

Jean Giraud

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Exercise the Mathcad bloc

#18 Pubblicato: 14/04/2022 20:19:07

overlord

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Wrote
Thank you all for the feedback, is there a literature or manual to explain the Mathcad block plugin?
Thanks

We have what Viacheslav provided us.
There are some samples or functions too which individual users uploaded.
You can look the extension page for some examples.
And there are some samples in forum topic that users posted.
It may be a small bunch, but we try to understand its capabilities.
This feature/plugin is also new to us.

Regards

https://en.smath.com/forum/yaf_postst726_Mathcad-Toolbox.aspx

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solving simultaneous equations with Solve - Solve() Maxima not working - Messaggi