I have to find the laplace inverse of a function y(s) which has repeated complex roots.(adsbygoogle = window.adsbygoogle || []).push({});

Y(s)=s^2 / (s^2+4)^2

so s=2i, s=2i, s=-2i, s=-2i.

My partial fraction is as follows:

A/(s-2i) + B/(s-2i)^2 + C/(s+2j) + D/(s+2j)^2

I use the standard method for finding regular repeated roots but I get stuck trying to calculating C and D. My values are undefined. My work is below...

A= d/ds[(s-2i)^2*Y(s)]=8s(3s^2-4)/(s^2+4)^3 + 4s^2(s^2-12)*i/(s^2+4)^3-->then you set s=2i which then results in A=-6i.

And B=1

But now for C, when I use the same process as A but instead of 2i, I use -2i, my answer is a number over 0 which results in undefined.

Am I even doing this problem correctly? Any help would be appreciated...

Thanks!

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# Homework Help: Please, ive been stuck on this inverse laplace for awhile

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