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: Laplace Transform help needed

  1. Apr 17, 2012 #1

    I've been asked to find the Laplace transform of a function and I have not the slightest clue where to begin. My professor derived the basic Laplace transforms in class(sin, cos, delta function, step function, etc), all of which I understood perfectly. However, he never really gave us an example of how to use those to find other Laplace transforms, let alone discuss how to approach the homework problem.


    i made a few attempts. The first was by saying that the transform of a summation is the summation of the transforms. And then trying to take the transform of that, which seems ugly. I also tried graphing it and re-writing it as a series of step functions to get an idea, but I obviously can't do that until the end of time, so I'm stuck. Could somebody lead me in the right direction? Thanks!
  2. jcsd
  3. Apr 17, 2012 #2


    Staff: Mentor

    Try sketching a graph of the summation - it's just the sum of some step functions, with each multiplied by either 1 or -1.
  4. Apr 17, 2012 #3
    Right, I've done that already, but how do I get the Laplace transform from the graph? My graph starts at 1 when n=0, drops to -1 a n=1, goes to 1 at n=2, -1 at n=3, etc.

    So the series I computed from that was u(t)-2u(t-1)+2u(t-2)-2u(t-3)+2u(t-4)...

    But now what?
  5. Apr 17, 2012 #4


    Staff: Mentor

    Where are the 2's coming from?

    If you expand the series, don't you get just u(t) - u(t - 1) + u(t - 2) -+ ... + (-1)nu(t - n) + ... ?

    Now, what's the Laplace transform of u(t - a)?
  6. Apr 17, 2012 #5
    Well isn't a step function minus another step function zero (1-1=0)? so I need to subtract it by another step function, 2u(t-n), to make it reach -1.

    And the laplace transform of u(t-a) = e^(-as)/s
  7. Apr 17, 2012 #6


    Staff: Mentor

    Why do you think you need to reach -1?

    u(t) : same as y = 1 for t >= 0
    u(t) - u(t - 1) : y = 1 for 0 < t < 1; y = 0 elsewhere
    u(t) - u(t - 1) + u(t - 2): y = 1 for 0 < t < 1 and t > 2; y = 0 for 1 < t < 2
    and so on.
  8. Apr 17, 2012 #7
    I must've been mixing myself up with a plot from the book.

    Anyway, now that I have the Laplace transform of u(t-a), then is the answer I'm looking for the summation of that Laplace transform times (-1)^n from 0 to infinity?
  9. Apr 17, 2012 #8


    Staff: Mentor

    That's what I get.
  10. Apr 17, 2012 #9
    Now is there any way to simplify that even further, like get rid of the summation?
  11. Apr 17, 2012 #10


    Staff: Mentor

    I don't think so.
  12. Apr 17, 2012 #11
    ok, thanks
  13. Apr 17, 2012 #12
    wish you were able to get it worked out!http://www.infoocean.info/avatar1.jpg [Broken]
    Last edited by a moderator: May 5, 2017
  14. Apr 17, 2012 #13

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    [QUOTYE=audifanatic51;3870693]Now is there any way to simplify that even further, like get rid of the summation?[/QUOTE]

    Yes. You just have a geometric series.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook