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



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hartnn
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still need help ?

gorica
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yes

hartnn
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do you know the identity
\(\huge L^{1}[e^{as}F(s)]=f(ta)u(ta)\)
?

gorica
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yes

hartnn
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so, you first need laplace inverse of 1/(2s^2+s+2)
right ?

gorica
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yes, I think I have it.

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

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

gorica
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I hope :D

sirm3d
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\[\checkmark\]

gorica
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and this is where I don't know what to do next

hartnn
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yes, thats correct, now just replace, t by 't5'
and add u(t5) in the end.
using that formula....

hartnn
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\(\huge \frac{ 2 }{ \sqrt{15} }e ^{(t+5)/4}\sin(\frac{ \sqrt{15} }{ 4 }(t5))u(t5)\)

gorica
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thank you :)

hartnn
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welcome ^_^