We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
93
3
avatar

how do you find the inverse Laplace transform of 5/(s-1)(s2+4)

 Sep 19, 2019
 #1
avatar+28190 
+2

"how do you find the inverse Laplace transform of 5/(s-1)(s2+4)"

 

Assuming the function of interest is  \(f(s)=\frac{5}{(s+1)(s^2+4)}\)

 

First expand as partial fractions:  \(f(s)=\frac{1}{s-1}-\frac{s}{s^2+4}-\frac{1}{s^2+4}\)

 

Then do the inverse Laplace transforms of these (the first term wil result in an exponential, the second will have the form of a cosine, and the third the form of a sine).

 Sep 19, 2019
 #2
avatar
+1

Thanks for your help.

Can you recommend anything to help me expand as partial fractions, please?

Guest Sep 19, 2019
 #3
avatar+28190 
+1

Try the following site: https://www.mathsisfun.com/algebra/partial-fractions.html

 

Incidentally, I’ve just noticed that in my original reply I had (s+1) in the denominator rather than (s-1). However, the same approach should be used, I.e. expand using partial fractions, then inverse Laplace each of the simpler fractions so obtained.

Alan  Sep 20, 2019

27 Online Users

avatar
avatar