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

1. hartnn

still need help ?

2. gorica

yes

3. hartnn

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

4. gorica

yes

5. hartnn

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

6. gorica

yes, I think I have it.

7. hartnn

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

8. gorica

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

9. gorica

I hope :D

10. sirm3d

$\checkmark$

11. gorica

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

12. hartnn

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

13. hartnn

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

14. gorica

thank you :)

15. hartnn

welcome ^_^