topic Re: Inverse Laplace Transform and Absolute Value in Mathcad

Inverse Laplace Transform and Absolute Value

DamienB — Tue, 18 Nov 2025 20:11:58 GMT

Currently using MathCAD v15 (M050). I have Prime 10 but am having licensing issues at the moment.

Anyway, I'm having trouble understanding why the invlaplace function won't evaluate as shown in the attachment. If I remove the absolute value sign, then it all works as expected (am I just running up against a domain issue and need to use the "assume" keyword.....or something......?)

Any advice is welcomed and appreciated! If Prime 10 has no problem with it, then that's my answer (just gotta lean on IT to get the license issues sorted).

Thanks!

Re: Inverse Laplace Transform and Absolute Value

Werner_E — Tue, 18 Nov 2025 20:52:42 GMT

Looks like what you demand is too hard for the symbolics in Mathcad.

Its also too hard for Prime's symbolics:

And Wolfram Alpha isn't able to come up with the desired result |sin(t)| either:

Re: Inverse Laplace Transform and Absolute Value

Werner_E — Tue, 18 Nov 2025 21:07:23 GMT

In Mathematics the absolute function is kind of a beast which usually is quite hard to handle.

Much more difficult like a simple function like the squaring

or even the Heaviside function

(we see "1" instead of "Phi(t)" because the result of course is valid only for t>=0).

We could try to rewrite the absolute value using the modulo function, but unfortunately the laplace operator can't deal with the modulo function

Re: Inverse Laplace Transform and Absolute Value

DamienB — Wed, 19 Nov 2025 14:17:36 GMT

Thank you for the response!

Re: Inverse Laplace Transform and Absolute Value

ttokoro — Sat, 22 Nov 2025 10:15:23 GMT

Re: Inverse Laplace Transform and Absolute Value

anursingh — Sun, 28 Dec 2025 18:00:12 GMT

Hi @DamienB,

I wanted to see if you got the help you needed.

If so, please mark the appropriate reply as the Accepted Solution. It will help other members who may have the same question.
Of course, if you have more to share on your issue, please pursue the conversation.

Thanks,
Anurag