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!

Homework Help: Finding inverse of a Laplace transform by convolution

  1. Oct 15, 2016 #1
    1. The problem statement, all variables and given/known data
    find the inverse Laplace transform of the given function by
    using the convolution theorem

    2. Relevant equations

    F(s) = s/((s+1)(s2)+4)

    The theorem : Lap{(f*g)(t)} = F(s)*G(s)
    3. The attempt at a solution
    I know how to find it the answer is :
    we have 1/(s+1) * s/(s+4) and the inverse of each of these functions are : e-t * cos(2t)
    further the answer is : ∫(e(-(t-τ))*cos(τ)dτ)
    But if I try to solve this problem without convolution theorem; and with partial fraction I get :

    s/((s+1)(s2+4)) = (1/5) ( (1/(s+1) + s/(s2+4) + 4/(s2+4) )

    and the inverse of this function is :

    (1/5) (cos(2t) - e-t +2sin(2t))


    ∫(e(-(t-τ))*cos(τ)dτ) = (1/5) (cos(2t) - e-t +2sin(2t)) is this right ?
  2. jcsd
  3. Oct 15, 2016 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What you wrote is not the convolution; the convolution is a definite integral, and you wrote an indefinite integral. In this method especially, limits are crucial.

    Anyway, in your integral you should have ##\cos(2 \tau) \, d \tau##, not ##\cos(\tau) \, d \tau##.

    After fixing things up, you will be able to answer your own question, by either (i) doing the integral; or (ii) differentiating both sides to see if the derivatives match.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted