My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
October 13th, 2013, 09:19 AM   #1
Joined: Oct 2013

Posts: 13
Thanks: 0

Inverse laplace transform

Hi, I am trying to do the inverse Laplace transform for this equation I arrived at with partial fractions. Two of the terms have complex numbers in them and I see that they are simplified to Cos and Sin terms from their exponential form (the process is quoted as 'Eulers identity'). Could somebody explain how this process is carried out?

L^-1 : 5*(-1+j)/(s+j500)

and 5*(-1-j)/(s+j500)

The inverse of these I have as (-1+j)e^(j500*t) and (-1-j)e^(-j500*t) respectively (I hope that is correct!)

Where my total equation is equal to these two terms and one other non-complex exponential term added together (it is for current in a resistor inductor circuit with a sinusoidal source voltage).

Many thanks,

Rydog21 is offline  
October 13th, 2013, 06:23 PM   #2
Senior Member
jks's Avatar
Joined: Jul 2012
From: DFW Area

Posts: 642
Thanks: 99

Math Focus: Electrical Engineering Applications
Re: Inverse laplace transform

Hi Rydog21,

I believe that you need to use Euler's Formula:

I also think that there is a mis-statement in your problem. The reason is that the denominators are both the same but the signs of the exponents in the Inverse Laplace Transform are opposite. I will assume that you meant to find:

Given that:

we get:


By Euler's formula, we can write as and

we can write as

Substituting these into the right hand side of equation [1] we get:

Using Euler's Formula again, this reduces to:

Since the imaginary terms cancel and the real terms add giving:

Note, of course, that could be replaced with
jks is offline  
October 15th, 2013, 10:35 AM   #3
Joined: Oct 2013

Posts: 13
Thanks: 0

Re: Inverse laplace transform

Thanks for that, I understand now. You're the man.
Rydog21 is offline  

  My Math Forum > College Math Forum > Calculus

inverse, laplace, transform

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Inverse Laplace transform Asmir Complex Analysis 2 August 18th, 2013 06:49 AM
inverse laplace transform capea Complex Analysis 5 August 3rd, 2013 03:30 PM
Laplace tranform and inverse of Laplace transform Deiota Calculus 1 April 28th, 2013 11:28 AM
inverse laplace transform defunktlemon Real Analysis 1 April 14th, 2012 03:19 PM
Inverse Laplace Transform timh Applied Math 1 June 7th, 2010 07:44 PM

Copyright © 2019 My Math Forum. All rights reserved.