1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Laplace Transform question

  1. Jul 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Laplace Transform of e-t sin t

    2. Relevant equations


    3. The attempt at a solution

    I have the solution, but I am unable to figure out how the denominator becomes 1/[(s + 1)2 + 1]
  2. jcsd
  3. Jul 20, 2011 #2


    User Avatar
    Homework Helper

    The presence of the eat would case the shift from 's' to 's-a'. This is why it is called the shift theorem, it's mainly used in the inverse laplace transform.

    So you know that L{sint} = 1/(s2+1)

    and following shift theorem L(eatsint) = 1/[(s-a)2+1].

    You can derive it too using the integral formula.
  4. Jul 20, 2011 #3
    I am unable to derive it from the integral formula. I need to see the steps. I'm fairly certain I've been able to integrate it correctly, but I keep getting a repetitive e^-t sin t or e^-t cos t when I integrate.
  5. Jul 20, 2011 #4
    So you're probably ending up with something like ∫e-t sin t dt on both sides of the equation; just move one to the other side and combine them as like terms. There's a good example of a similar problem on Wikipedia with ∫ex cos x dx:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Laplace Transform question Date
Quick laplace transform question Oct 19, 2015
Laplace Transform question with unit step function May 7, 2015
Laplace transformation question Apr 24, 2015
Laplace Transform Question Dec 31, 2013
LaPlace Transform question #2 Apr 13, 2013