1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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 Notational Question

  1. Feb 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Given: [tex]\frac{d^2y}{dt^2} + 12\frac{dy}{dt} + 32y = 32u(t)[/tex]

    and that all initial conditions are zero, use the Laplace transform to find y(t)

    This is an example problem from my text. They start the solution by taking the Laplace of both sides assuing y'(0) = 0 & y(0) = 0 :

    [tex]s^2Y(s) + 12sY(s) + 32Y(s) = \frac{32}{s}[/tex]

    I am just a little confused why [itex]L[32y] = Y(s)[/itex] but [itex]L[32u(t)] = 32/s[/itex]

    y is a function of time, so why is y(t) treated differently from u(t)?

    I know this is probably a stupid question...sorry :redface:

  2. jcsd
  3. Feb 5, 2010 #2
    Sorry! I think I got it! I just found in my notes that some texts denote the 'unit step function' u(t). Where u(t) = 1 for t >0 and u(t) = 0 for t<=0.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook