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 question

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data


    this one stumped me..

    d^2y/dt^2 +ωy=ksin((√ω)t)

    y(∏/4)=0, y'(∏/4)=0




    3. The attempt at a solution

    → (s^2 + ω)U(s)= LT {ksin((√ω)(T+∏/4)} is as far as i can get (i know what to do with the left hand side once i get the LT of the right hand side but i dont know what to do with the sin value)
     
  2. jcsd
  3. Nov 23, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What is "T"? Did you mean "t"?

    I presume you know the definition:
    [tex]L(f(t))= \int_0^\infty e^{-st}f(s)dx[/tex]

    Here that woud be
    [tex]\int_0^\infty e^{-st}(k sin(\sqrt{\omega}(t+ \pi/4))dt[/tex]

    The substitution v= [itex]\sqrt{\omega}(t+ \pi/4)[/itex] reduces that to a fairy straight forward "integration by parts" but you should also have formulas for the Laplace transform of sin(x) as well as for f(x+ a) in terms of the Laplace transform of f(x).
     
  4. Nov 24, 2012 #3
    well, i would normally use tau but i couldnt find symbol, so i just used T to distinguish from t

    doing this by integration by parts ends with a complicated (a) (from sin at) that is impossible to break down into to a/s^2+a^2 (LT formula) ...if it were just sin√wt then i get it..but i am missing some step
     
    Last edited: Nov 24, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Laplace Transform question
Loading...