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!

Initial value problem

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve IVP
    y'' + 2y' + 2y = u_pi(t) + u_2pi(t)
    with IC
    y(0) = 0 and y'(0) = 1.


    2. Relevant equations
    L{f''(t)} = s^2Y(s) - sy(0) - y'(0)
    u_c(t) = u(t-c) -->Laplace--> e^-cs/s


    3. The attempt at a solution
    y'' + 2y' + 2y = u_pi(t) + u_2pi(t)
    y'' + 2y' + 2y = u(t-pi) + u(t-2pi)
    L{y'' + 2y' + 2y} = e^(-pis)/s + e^(-2pis)/s

    s^2Y(s) - sy(0) - y'(0) + 2[sY(s)-y(0)] +2Y(s) = e^(-pis)/s + e^(-2pis)/s
    s^2Y(s) - 1+ 2sY(s) +2Y(s) = e^(-pis)/s + e^(-2pis)/s
    Y(s)(s^2 + 2s +2) = e^(-pis)/s + e^(-2pis)/s + 1
    Y(s)((s+1)^2) = e^(-pis)/s + e^(-2pis)/s + 1
    Y(s) = e^(-pis)/(s(s+1)^2) + e^(-2pis)/(s(s+1)^2) + 1/((s+1)^2)


    before going any further though, I have hunch that the laplace of RHS is incorrect.. it looks correct when i compare it to the equation im using (above) but I am wondering when or under what circumstances the denominator of e^-cs/s can change (ie, become squared or something like that)?
    thanks for any help
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  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?