How to calculate inverse Laplace transform of (7s^2+3s+5)/((s^2−4s+29)(s^2+25))?

demitereur 2022-09-26 Answered
How to calculate inverse Laplace transform of 7 s 2 + 3 s + 5 ( s 2 4 s + 29 ) ( s 2 + 25 ) ?
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Answers (1)

Marley Stone
Answered 2022-09-27 Author has 13 answers
Note that
A s + B s 2 + 5 2 = A / 2 i B / 10 s 5 i + A / 2 + i B / 10 s + 5 i
has inverse Laplace transform
( A / 2 i B / 10 ) e 5 i t + ( A / 2 + i B / 10 ) e 5 i t = A cos 5 t + B 5 sin 5 t .
Since s 2 4 s + 29 = ( s 2 ) 2 + 5 2 , the other partial fraction admits a similar analysis.
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