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JBlackhole16-Pearl
16-Pearl
December 6, 2021
Solved

Inverse Laplace - simplification?

  • December 6, 2021
  • 1 reply
  • 2039 views

to all,

Attached is a 1st test of using mcad15 inverse Laplace. While I get something, is there a way of getting a “neater” response out of mcad15? For example mcad15 returns sqrt(wf^2) – why not wf ? I think one can end up getting imaginary numbers if one uses specific values !

I know some of the regular users are very handy at using Laplace operations so maybe I might get a few tips and/or tricks

Thanks

[correction: a square was missing!]

Best answer by Werner_E
For example mcad15 returns sqrt(wf^2) – why not wf ?

Because sqrt(x^2)=x is not valid for all numbers x - think of x=-1.

You may fix this by adding "assume, omega.f>0" or, maybe better, "assume, ALL>0" if that applies.

Also adding "simplify" or even (more time consuming) "simplify,max" may help a bit.

Rewriting the hyperbolic sine and cosine could be done by adding "rewrite, e".

But generally we can say that modifying the output of Mathcads symbolic results always was a PITA and a matter of trial and error and despair.

Here are a few attempts of mine, none resulted in a much simpler result. When I tried to substitute the root expression for W*1i I noticed that Mathcad did not substitute all occurrences of the root and only a second substitute command did the job. As I said - trial, error and pain 😞

Werner_E_0-1638809879355.png

 

1 reply

W
Werner_E25-Diamond IAnswer
25-Diamond I
December 6, 2021
For example mcad15 returns sqrt(wf^2) – why not wf ?

Because sqrt(x^2)=x is not valid for all numbers x - think of x=-1.

You may fix this by adding "assume, omega.f>0" or, maybe better, "assume, ALL>0" if that applies.

Also adding "simplify" or even (more time consuming) "simplify,max" may help a bit.

Rewriting the hyperbolic sine and cosine could be done by adding "rewrite, e".

But generally we can say that modifying the output of Mathcads symbolic results always was a PITA and a matter of trial and error and despair.

Here are a few attempts of mine, none resulted in a much simpler result. When I tried to substitute the root expression for W*1i I noticed that Mathcad did not substitute all occurrences of the root and only a second substitute command did the job. As I said - trial, error and pain 😞

Werner_E_0-1638809879355.png

 

    J
    JBlackhole16-PearlAuthor
    16-Pearl
    December 7, 2021

    an attempt with Wolfram online calculator (w is wf and w1 is wn)

    laplaceinverse_wolfram - Copy.png

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