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!

A couple laplace transforms, need help

  1. Apr 14, 2007 #1
    1. The problem statement, all variables and given/known data
    just a small part of a large problem ><a im not even sure if this is in the right place. the first two questions i have to ask are really minor so i didnt want to make separate threads for each one. the third one is an actual problem itself tho.

    (1) i need the laplace inverse of :
    [s^2]/[s^2 - 3^2]
    -solved, there was an error at the start that threw the rest of my eqn off. there is no s^2

    (2) laplace transformation of:
    - solved

    (3) find laplace inverse of:
    F(s) = [3*e^(-4s)] / [s*(s^2 + s + 5/4)]

    2. Relevant equations
    for the second one, the u comes from working with time intervals using the second shift theorem
    which is: (L(g(t - k)u(t - k)) = e^(-k*s)*G(s)
    where G(s) is the laplace transform of of g(t)
    the third question also uses

    3. The attempt at a solution

    for the first one, i have no idea of how to even look at this because i've been using a laplace conversion sheet to solve them all up until now. the only laplace transformation i've seen with s^2 in the numerator looks just like the problem i have here but the intire denominator is squared awell.. other than that i cant find a laplace transform to matchit. -solved

    the second one seems simple enough but im stuck. it was originally part of another function i had to laplace, but it was too complicated to laplace as it was and i singled that much out. the original term was:

    (t - 2)u(t - 3) and so i broke this into smaller terms so thati could use the second shifting theorem on one of the termsand got:

    (t - 3)u(t - 3) + u(t - 3)
    [im leaving out the multiplication "*" signs so its easier to look at]

    then that laplaced to:

    e^(-3*s)/[s^2] + [the laplace of the second term]

    im not quite sure whether this just counts as one and laplaces to (1/s) or something.

    for question three i took out the e and its power because the -4*s would be used for the second shifting theorem. leaving 3/[s*(s^2 + s + 5/4)]

    from here i tried to use partial fractions on the equation to make it easier, but i keep ending up getting 2 different values for my first variable.

    also with the (s^2 + s + 5/4) i perfected the square to:
    [(s + 1/2)^2 + 1]

    if i could work the partial fraction for this, i might beable to solve the laplace inverses for the single terms, using the laplace transformation chart. so the main problem is the partial fraction.
    i had to "un-perfect the square" to make this part easier

    what i have for that is:
    3/[s*(s^2 + s + 5/4)] = A/s + B*(s^2 + s + 5/4)
    3/[s*(s^2 + s + 5/4)] = [A*(s^2 + s + 5/4) + B*s] / [s*(s^2 + s + 5/4)]
    3 = A*(s^2 + s + 5/4) + B*s
    3 = A*s^2 + A*s + A*5/4 + B*s
    3 = A*s^2 + (A+B)*s + A*5/4

    this is what is giving me two separate values for A,
    where due to the first term, A must equal zero.
    but due to the second term A must equal to 12/5.

    thanks if you can help

    edit: i clicked off of the form without realising and accidentally submit. i think.
    Last edited: Apr 14, 2007
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?

Similar Discussions: A couple laplace transforms, need help