
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 6th, 2015, 01:09 PM  #1 
Senior Member 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 = 1.7243e04 B = 1.3440e10 C = 1.7243e04 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 01:19 PM. 
April 7th, 2015, 06:30 AM  #2 
Senior Member Joined: Oct 2014 From: EU Posts: 224 Thanks: 26 Math Focus: Calculus 
I solved.. My error was not considering the 1.034e4 coefficient.. 

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 01:38 PM 
confused...  najaa  Calculus  3  April 13th, 2012 02:41 AM 
A bit confused  Valar30  Advanced Statistics  2  September 14th, 2011 11:02 AM 
trying to make a solution (liquid solution...) problem...  TreeTruffle  Algebra  2  March 27th, 2010 01:22 AM 
confused  mikeportnoy  Applied Math  1  December 31st, 1969 04:00 PM 