solving simultaneous equations with Solve

#1 Posted: 3 years ago

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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 not found.File not found.

#2 Posted: 3 years ago

sergio

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Show Spoiler

test_sergio.sm (8 KiB) downloaded 99 time(s).
sergio

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Mo 3 years ago

#3 Posted: 3 years ago

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 KiB) downloaded 96 time(s).

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Mo 3 years ago

#4 Posted: 3 years ago

Mo

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Thanks Overlord, PompelmoTell, greatly appreciated!!

#5 Posted: 3 years ago

⚜ 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 3 years ago

#6 Posted: 3 years ago

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 KiB) downloaded 78 time(s).

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sergio 3 years ago, Mo 3 years ago

#7 Posted: 3 years ago

Jean Giraud

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...

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Fridel Selitsky 3 years ago

#8 Posted: 3 years ago

Jean Giraud

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... more in there from native Smath code.

Solve FindRoot FORUM.sm (10 KiB) downloaded 90 time(s).

#9 Posted: 3 years ago

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 KiB) downloaded 89 time(s).

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Mo 3 years ago

#10 Posted: 3 years ago

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 KiB) downloaded 90 time(s).

There is also this way for guess define.

#11 Posted: 3 years ago

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 Posted: 3 years ago

Martin Kraska

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

mathblock_Solve.sm (4 KiB) downloaded 91 time(s).

Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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sergio 3 years ago

#13 Posted: 3 years ago

⚜ 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 Posted: 3 years ago

Alvaro Diaz Falconi

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

isol_example.sm (68 KiB) downloaded 100 time(s).
isol_example.pdf (34 KiB) downloaded 80 time(s).

Best regards.
Alvaro.

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sergio 3 years ago

#15 Posted: 3 years ago

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 Posted: 3 years ago

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 KiB) downloaded 86 time(s).

#17 Posted: 3 years ago

Jean Giraud

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Exercise the Mathcad bloc

#18 Posted: 3 years ago

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 - Messages