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gorica

  • 2 years ago

I need help in finding inverse Laplace transformation of e^(-5s)/(2s^2+s+2)

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  1. hartnn
    • 2 years ago
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    still need help ?

  2. gorica
    • 2 years ago
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    yes

  3. hartnn
    • 2 years ago
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    do you know the identity \(\huge L^{-1}[e^{-as}F(s)]=f(t-a)u(t-a)\) ?

  4. gorica
    • 2 years ago
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    yes

  5. hartnn
    • 2 years ago
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    so, you first need laplace inverse of 1/(2s^2+s+2) right ?

  6. gorica
    • 2 years ago
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    yes, I think I have it.

  7. hartnn
    • 2 years ago
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    ohh...so you were able to find laplace inverse of 1/(2s^2+s+2) ??

  8. gorica
    • 2 years ago
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    yes. It's this \[\frac{ 2 }{ \sqrt{15} }e ^{-t/4}\sin(\frac{ \sqrt{15} }{ 4 }t)\]

  9. gorica
    • 2 years ago
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    I hope :D

  10. sirm3d
    • 2 years ago
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    \[\checkmark\]

  11. gorica
    • 2 years ago
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    and this is where I don't know what to do next

  12. hartnn
    • 2 years ago
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    yes, thats correct, now just replace, t by 't-5' and add u(t-5) in the end. using that formula....

  13. hartnn
    • 2 years ago
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    \(\huge \frac{ 2 }{ \sqrt{15} }e ^{(-t+5)/4}\sin(\frac{ \sqrt{15} }{ 4 }(t-5))u(t-5)\)

  14. gorica
    • 2 years ago
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    thank you :)

  15. hartnn
    • 2 years ago
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    welcome ^_^

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