Thread: What is the inverse Laplace transormation of this please?

Hi I'm trying to work out the inverse Laplace transform of 4/[(s-2)^2 + 16]

Could anyone help please? I have tried factorising the denominator part which can also be written as s^2 - 4s + 20 but aren't there only surd factors to satisfy this? I think I'm better leaving it in its original completed square form but I'm if I do I'm not sure how to go about doing the partial fractions stage to find a standard inverse transform...

you have to split the denominator in (s-2-4i)(s-2+4i)

Originally Posted by chunkylumber111

Hi I'm trying to work out the inverse Laplace transform of 4/[(s-2)^2 + 16]

Could anyone help please? I have tried factorising the denominator part which can also be written as s^2 - 4s + 20 but aren't there only surd factors to satisfy this? I think I'm better leaving it in its original completed square form but I'm if I do I'm not sure how to go about doing the partial fractions stage to find a standard inverse transform...

Thanks Prove It, that's a great help. Is there an intermediate step you did to get e^2t L^-1 (4/s^2 + 4^2)?

Originally Posted by chunkylumber111

Thanks Prove It, that's a great help. Is there an intermediate step you did to get e^2t L^-1 (4/s^2 + 4^2)?

It's the horizontal shifting theorem.

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