gorica
  • gorica
I need help in finding inverse Laplace transformation of e^(-5s)/(2s^2+s+2)
Differential Equations
katieb
  • katieb
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hartnn
  • hartnn
still need help ?
gorica
  • gorica
yes
hartnn
  • hartnn
do you know the identity \(\huge L^{-1}[e^{-as}F(s)]=f(t-a)u(t-a)\) ?

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gorica
  • gorica
yes
hartnn
  • hartnn
so, you first need laplace inverse of 1/(2s^2+s+2) right ?
gorica
  • gorica
yes, I think I have it.
hartnn
  • hartnn
ohh...so you were able to find laplace inverse of 1/(2s^2+s+2) ??
gorica
  • gorica
yes. It's this \[\frac{ 2 }{ \sqrt{15} }e ^{-t/4}\sin(\frac{ \sqrt{15} }{ 4 }t)\]
gorica
  • gorica
I hope :D
sirm3d
  • sirm3d
\[\checkmark\]
gorica
  • gorica
and this is where I don't know what to do next
hartnn
  • hartnn
yes, thats correct, now just replace, t by 't-5' and add u(t-5) in the end. using that formula....
hartnn
  • hartnn
\(\huge \frac{ 2 }{ \sqrt{15} }e ^{(-t+5)/4}\sin(\frac{ \sqrt{15} }{ 4 }(t-5))u(t-5)\)
gorica
  • gorica
thank you :)
hartnn
  • hartnn
welcome ^_^

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