Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Laplace Inverse Problem

  1. Nov 12, 2006 #1
    I am trying to do the inverse of the foll. eqn. to no avail:

    s+1/(s^3 + s + 1)

    I cannot factorise the denominator.
    My only alternative was to use the defintion of Laplace and try to integrate the equation. Still I could not. Can anyone provide some hints?
     
  2. jcsd
  3. Nov 12, 2006 #2
    That function in the denominator is cubic so it atleast has one real root. After graphing it, I can see that it has 1 real root. Hence, it has two complex roots. My guess would be to write that polynomial as a product of one real factor and two complex factors. I have no idea how to do that though.

    It is a tough one though! I hope someone else in this forum is able to help you.
     
    Last edited: Nov 12, 2006
  4. Nov 13, 2006 #3
    Actually, you can use the Cardano's method to find the exact roots.

    Numerically, though, the roots are:
    .341 + 1.16j; .341-1.16j; and -.682

    Now you can treat these complex numbers just like any other real numbers and do the partial fraction expansion.
     
  5. Nov 19, 2006 #4
    Factor out the real root, then preform partial fractions on the denominator, split up your expression into two, and solve.

    Regards,

    Nenad
     
  6. Nov 22, 2006 #5
    Thanks, I just could not find a standard method to factorise the denominator.
     
  7. Dec 7, 2006 #6
    Hi, I need some help!

    I performed inverse laplace on (s^2+5s+6)/(s^3-s^2+2) and got 3/5*e^t*cos(t)+29/5*e^t*sin(t)+2/5*e^-t. My question is how do you take it back to the differential equation and how do you tell what type of differential equation it is?
     
  8. Dec 7, 2006 #7
    hmm why would you want to?

    if you used a laplace transform than it must have been a linear differential equation, combined with an initial value problem.

    also because the highest power of s is s^3 I'd say that it couldn't have been more than third order. (although there might be special circumstances that I'm missing.)

    I don't believe there is enough information to easily reconstruct the differential equation.
     
  9. Dec 7, 2006 #8
    Is there a way to approximate the differential equation?
     
  10. Dec 7, 2006 #9
    none that I know of, part of your problem is that you don't know what the original driving function was, or the initial conditions.

    because a laplace transform depends on both of these things its impossible to determine what the differential equation was.

    but once again why would you want to reconstruct the differential equation?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?