inverse Laplace Transform: (7s^2+20s+53)/[(s-1)(s^2+2s+5)]

mathstresser

Junior Member
Joined
Jan 28, 2006
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134
Find the inverse Laplace Transform:

\(\displaystyle \L\\ \frac{7s^2\, +\, 20s\, +\, 53}{(s\, -\, 1)(s^2\, +\, 2s\, +\, 5)}\)

I can set that eqaul to:

\(\displaystyle \L\\ \frac{A}{s\, -\, 1}\, +\, \frac{Bs\, +\, C}{s^2\, +\, 2s\, +\, 5}\)

The first part I would get:

\(\displaystyle \L\\ Ae^{1t}\)

for the next part do I split it up and get:

\(\displaystyle \L\\ \frac{Bs}{s^2\, +\, 2s\, +\, 5}\, +\, \frac{C}{s^2\, +\, 2s\, +\, 5}\)

What do I do now?
 
\(\displaystyle \L\\\frac{7s^{2}+20s+53}{(s-1)(s^{2}+2s+5)}=\frac{10}{s-1}-\frac{3}{s^{2}+2s+5}-\frac{3s}{s^{2}+2s+5}\)
 
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