Question

Find the inverse Laplace transform of \begin{equation} F(s) = \frac{e^{-6s}}{s^2 + 1s - 12} \end{equation} \begin{equation} f(t) = (t - 6) \left(\frac{1}{7}e^{3(t-6)} - \frac{1}{7}e^{-4(t-6)}\right) \text{ (Use step(t-a) for } u_a(t) ) \end{equation}

          Find the inverse Laplace transform of
\begin{equation} 
F(s) = \frac{e^{-6s}}{s^2 + 1s - 12}
\end{equation}
\begin{equation} 
f(t) = (t - 6) \left(\frac{1}{7}e^{3(t-6)} - \frac{1}{7}e^{-4(t-6)}\right) \text{ (Use step(t-a) for } u_a(t) )
\end{equation}
        
Show more…
Find the inverse Laplace transform of

    F(s) = (e^-6s)/(s^2 + 1s - 12)


    f(t) = (t - 6) ((1)/(7)e^3(t-6) - (1)/(7)e^-4(t-6))  (Use step(t-a) for  ua(t) )

Added by Anthony B.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Find the inverse Laplace transform of f(t) = 26e^(34t) * u(t-a)
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn David Collins
Jennifer Stoner verified

Sri K and 63 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
point-find-the-inverse-laplace-transform-of-fs-s2-_-2s-8-fw-use-stept-c-for-uzt-09044

Find the inverse Laplace transform of F(s) = e^(-6s) / (s^2 - 2s - 8) f(t) = (Use step(t-c) for u_c(t) .)

Sri K.

find-the-inverse-laplace-transform-ft-of-fs-14497

Find the inverse Laplace transform f(t) of F(s)

Avinash V.

find-the-given-inverse-laplace-transform-by-finding-the-laplace-transform-of-the-indicated-functio-2-72136

Find the given inverse Laplace transform by finding the Laplace transform of the indicated function $f.$ $$\mathscr{L}^{-1}\left\{\frac{1}{s^{2}\left(s^{2}+a^{2}\right)}\right\} ; f(t)=a t-\sin a t$$

Arjun S.


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,172 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,664 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,196 solutions

*

Transcript

-
00:01 Hi, in this question we have been given a function f of s equal to e raised to the power minus 6s divided by s square minus 2s minus 8 and we need to find the laplace inverse of this function.
00:21 So here let us consider that g of s is equal to 1 divided by s square minus 2s minus 8.
00:33 So now we can write this as 1 divided by s square minus 4s plus 2s minus 8.
00:42 Again we can write this as 1 divided by, so here if you take s common so this will be s minus 4 and then here if you take 2 common so this will be 2 times s minus 4.
00:56 So finally we can write g of s will be equal to 1 divided by s minus 4 multiplied by s plus 2.
01:05 So again we can write gs equal to 1 divided by s minus 4 then minus 1 divided by s plus 2.
01:19 So if we do this then we will get 6 in the numerator therefore we need to multiply by 1 divided by 6 so that numerator will become 1.
01:29 So we have got the value of this gs...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever