My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 6th, 2015, 02:09 PM   #1
szz
Senior Member
 
szz's Avatar
 
Joined: Oct 2014
From: EU

Posts: 224
Thanks: 26

Math Focus: Calculus
Confused on the solution of an ILT

Hi all !

I am trying to compute the Inverse Laplace Transform of the transfer function:

$\displaystyle {(5\cdot 10^6 + 1.1s) \over (1.034\cdot10^{-4})s^3 + 470.4s^2 + 3\cdot10^{6}s}$

and the poles are:

$\displaystyle \begin{aligned}
& s = 0\\
& s_1 = -4542936.50 = -\alpha\\
& s_2 = -6382.98 = -\beta
\end{aligned}$


I wrote down the system of equations:

$\displaystyle \begin{aligned}
& {(5\cdot 10^6 + 1.1s) \over (1.034\cdot10^{-4})s^3 + 470.4s^2 + 3\cdot10^{6}s}\\
& {(5\cdot 10^6 + 1.1s) \over s(s + \alpha)(s + \beta)} = {A \over s} + {B \over (s + \alpha)} + {C \over (s + \beta)}\\
& (5\cdot 10^6 + 1.1s) = A(s^2 + s(\alpha + \beta) + \alpha\beta) + B(s^2 + \beta s)+ C(s^2 + \alpha s)\\
\\

& 0 = A + B + C \\
& 1.1 = A(\alpha + \beta) + B\beta + C\alpha\\
& 5\cdot 10^6 = A(\alpha\beta)

\end{aligned}$


And applying Cramer I obtain:

A = 1.7243e-04
B = 1.3440e-10
C = -1.7243e-04


But when I put these numbers into wolfram alpha as input:

partial fractions ( 5000000 + 1.1s )/(3000000s + 470.44s^2 + 0.0001034s^3)


The result is quiet different..

$\displaystyle {1.66667\over s}-{1.66667 \over (6385.97+s)}+{(1.09963×10^-6) \over (4.54332×10^6+s)}$

I don't understand where I am wrong.

Thank you in advance.

Last edited by szz; April 6th, 2015 at 02:19 PM.
szz is offline  
 
April 7th, 2015, 07:30 AM   #2
szz
Senior Member
 
szz's Avatar
 
Joined: Oct 2014
From: EU

Posts: 224
Thanks: 26

Math Focus: Calculus
I solved..

My error was not considering the 1.034e-4 coefficient..

szz is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
confused, ilt, solution



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help!! A.s.a.p. I'm really confused! Josh Algebra 2 November 13th, 2013 02:38 PM
confused... najaa Calculus 3 April 13th, 2012 03:41 AM
A bit confused Valar30 Advanced Statistics 2 September 14th, 2011 12:02 PM
trying to make a solution (liquid solution...) problem... TreeTruffle Algebra 2 March 27th, 2010 02:22 AM
confused mikeportnoy Applied Math 1 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.