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August 18th, 2013, 01:39 AM   #1
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Inverse Laplace transform

Could someone find inverse Laplace transform from:



I've tried solving it using convolution theorem but it seems like a fair amount of work for an school exam problem, so I thought there should be some easier soulution.
Thanks.
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August 18th, 2013, 03:51 AM   #2
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Re: Inverse Laplace transform

The poles are

Now, use

Find the residues at for and add them.

Your solution will pop out.

i.e. the residue at is

Find the residue for and add to this one. You have the inverse LaPlace.

Of course, you can write it in terms of sin(t) and cos(t).
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August 18th, 2013, 05:49 AM   #3
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Re: Inverse Laplace transform

I didn't even consider that aproach. :/
Thanks a lot.
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