Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
behzad24b
Group Title
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 .
 one year ago
 one year ago
behzad24b Group Title
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 .
 one year ago
 one year ago

This Question is Open

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

oldrin.bataku Group TitleBest ResponseYou've already chosen the best response.1
When 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 \(s\).
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
\[\begin{align*} \mathcal L \big\{ e ^{5x}f(x) \big\}\\ &=\int\limits_0^\infty e^{5x}f(x)e^{sx}\mathrm dx\\ &=\int\limits_0^\infty f(x)e^{(s5)x}\mathrm dx\\ \text{let }s5=p\\ &=\int\limits_0^\infty f(x)e^{px}\mathrm dx\\ &=F(p)\\ p=s5\\ &= F(s5)\end{align*}\]
 one year ago
See more questions >>>
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.