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

Sep 19, 2019

#1
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"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
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Can you recommend anything to help me expand as partial fractions, please?

Guest Sep 19, 2019
#3
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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