1. Not finding help here? Sign up for a free 30min 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

  1. Jul 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Use the Laplace Transform to solve: y"+2y'+2y=t y(0)=y'(0)=1


    2. Relevant equations
    L{y(t)} = Y(s)
    L{y'(t)} = sY(s)-y(s)
    L{y"(t)} = s2Y(s)-sy(0)-y'(0)
    using the laplace transform table: tn = n!/(sn+1) where n=1


    3. The attempt at a solution
    Take laplace on both sides:
    L{y"(t)} + 2L{y'(t)} + 2L{y(t)} = L{t}
    s2Y(s) - sy(0) - y'(0) + 2[sY(s)-y(0)] + 2Y(s) = 1/s2

    after plugging in the initial conditions I get:
    s2Y(s) - s - 3 + 2sY(s) + 2Y(s) = 1/s2

    isolate Y(s):
    Y(s)[s2+2s+2] = 1/s2 + s + 3
    Y(s) = (1/s2 + s + 3) / (s2+2s+2)
    I completed the square in the denominator to get: (m+1)2+1

    Y(s) = s / [(s2+1)(s+3)2-8]}

    Take the Laplace inverse
    L-1{ s / [(s2+1)(s+3)2-8]}

    I add and subtract 3 in the numerator to get:
    L-1{ (s+3)-3 / [(s2+1)(s+3)2-8]}

    Use linearity property of inverse transform to get from L-1{Y(s)} to y(t):
    L-1{ (s+3) / [(s2+1)(s+3)2-8]} - 3L-1{ 1 / [(s2+1)(s+3)2-8}

    How do I apply partial fraction decomposition to get y(t)?
     
    Last edited: Jul 30, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Laplace Transform
  1. Laplace transform (Replies: 0)

Loading...