solving simultaneous equations with Solve

#1 Posted: 4/5/2022 3:45:27 PM

0 likes in 34 posts.

Group: User

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: 4/5/2022 4:39:40 PM

sergio

115 likes in 329 posts.

Group: User

Show Spoiler

test_sergio.sm (8 KiB) downloaded 44 time(s).
sergio

1 users liked this post

Mo 4/5/2022 10:22:00 PM

#3 Posted: 4/5/2022 6:24:50 PM

overlord

549 likes in 1332 posts.

Group: Moderator

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 39 time(s).

1 users liked this post

Mo 4/5/2022 10:22:00 PM

#4 Posted: 4/5/2022 10:22:48 PM

Mo

0 likes in 34 posts.

Group: User

Thanks Overlord, PompelmoTell, greatly appreciated!!

#5 Posted: 4/6/2022 10:28:07 AM

⚜ Kenny Lemens, P.E. ᵂᴵ

74 likes in 164 posts.

Group: User

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

1 users liked this post

Mo 4/6/2022 11:57:00 AM

#6 Posted: 4/6/2022 11:40:36 AM

Fridel Selitsky

520 likes in 451 posts.

Group: User

If the damping coefficients are denoted by α1 and α2, you can use the function al_nlegsoive
test.sm (6 KiB) downloaded 26 time(s).

2 users liked this post

sergio 4/6/2022 12:26:00 PM, Mo 4/6/2022 11:57:00 AM

#7 Posted: 4/7/2022 11:08:53 AM

Jean Giraud

983 likes in 6866 posts.

Group: User

...

1 users liked this post

Fridel Selitsky 4/7/2022 11:54:00 AM

#8 Posted: 4/7/2022 1:43:03 PM

Jean Giraud

983 likes in 6866 posts.

Group: User

... more in there from native Smath code.

Solve FindRoot FORUM.sm (10 KiB) downloaded 28 time(s).

#9 Posted: 4/7/2022 5:27:55 PM

overlord

549 likes in 1332 posts.

Group: Moderator

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

mathblock.sm (5 KiB) downloaded 34 time(s).

1 users liked this post

Mo 4/9/2022 10:28:00 PM

#10 Posted: 4/7/2022 6:19:34 PM

overlord

549 likes in 1332 posts.

Group: Moderator

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 29 time(s).

There is also this way for guess define.

#11 Posted: 4/8/2022 2:19:42 AM

Fridel Selitsky

520 likes in 451 posts.

Group: User

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: 4/8/2022 8:04:07 PM

Martin Kraska

1222 likes in 2150 posts.

Group: Moderator

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

mathblock_Solve.sm (4 KiB) downloaded 33 time(s).

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

1 users liked this post

sergio 4/9/2022 4:48:00 AM

#13 Posted: 4/11/2022 9:57:44 AM

⚜ Kenny Lemens, P.E. ᵂᴵ

74 likes in 164 posts.

Group: User

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: 4/11/2022 4:44:08 PM

Alvaro Diaz Falconi

992 likes in 1674 posts.

Group: User

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

isol_example.sm (68 KiB) downloaded 40 time(s).
isol_example.pdf (34 KiB) downloaded 25 time(s).

Best regards.
Alvaro.

1 users liked this post

sergio 4/12/2022 5:01:00 AM

#15 Posted: 4/14/2022 12:10:17 PM

Mo

0 likes in 34 posts.

Group: User

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

#16 Posted: 4/14/2022 2:54:00 PM

Jean Giraud

983 likes in 6866 posts.

Group: User

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 20 time(s).

#17 Posted: 4/14/2022 7:43:45 PM

Jean Giraud

983 likes in 6866 posts.

Group: User

Exercise the Mathcad bloc

#18 Posted: 4/14/2022 8:19:07 PM

overlord

549 likes in 1332 posts.

Group: Moderator

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

SMath Forum

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