A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
can anyone say one or more samples for this Laplace tarnsform (with step by step solving) :
L{(e^ax) f(x)} = F(sa)
and what means sa exactly ? i cant understand that .
 2 years ago
can anyone say one or more samples for this Laplace tarnsform (with step by step solving) : L{(e^ax) f(x)} = F(sa) and what means sa exactly ? i cant understand that .

This Question is Open

behzad24b
 2 years ago
Best ResponseYou've already chosen the best response.0\[L \left\{ e ^{ax}f(x) \right\} = F(sa)\]

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1When dealign with Laplace transforms, it's useful to think of a *transformation* from the timedomain (t represents a time) to the *frequencydomain* (s represents a complex angular frequency, r e^(it))... in this case, multiplying by \(e^{ax}\) translates to a shift of the frequency \(s\).

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\begin{align*} \mathcal L \big\{ e ^{5x}f(x) \big\}\\ &=\int\limits_0^\infty e^{5x}f(x)e^{sx}\mathrm dx\\ &=\int\limits_0^\infty f(x)e^{(s5)x}\mathrm dx\\ \text{let }s5=p\\ &=\int\limits_0^\infty f(x)e^{px}\mathrm dx\\ &=F(p)\\ p=s5\\ &= F(s5)\end{align*}\]
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.