Convert the following equation from Laplace domain to continuous time domain: F(s)=(-2mkvR)/(2mRs^2+mks+2kR) m, k, v, R are all constants.

katdoringlo 2022-09-13 Answered
Need to convert the following equation from Laplace domain to continuous time domain:
F ( s ) = 2 m k v R 2 m R s 2 + m k s + 2 k R
m, k, v, R are all constants.
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Answers (2)

Kristopher Beard
Answered 2022-09-14 Author has 18 answers
It is a quadratic in s, so you can factor it using the quadratic formula.
2 m R s 2 + m k s + 2 k R = 0 s = 1 4 m R ( m k ± m 2 k 2 16 m k R 2 )   so   2 m R s 2 + m k s + 2 k R = 2 m R ( s 1 4 m R ( m k m 2 k 2 16 m k R 2 ) ) ( s 1 4 m R ( m k + m 2 k 2 16 m k R 2 ) )
and you can use partial fractions.

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sooxicyiy
Answered 2022-09-15 Author has 3 answers
First, use the quadratic formula to find the roots of the denominator and write F(s) in the following form:
F ( s ) = C ( s a ) ( s b ) .
If a=b, you are done. Otherwise, the partial fraction expansion will be
F ( s ) = C ( s a ) ( s b ) = C b a ( 1 s a 1 s b ) .

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