## RolyPoly 2 years ago $L^{-1} (\frac{2s^3}{s^2-81})$ The actual problem in the problem set is $L^{-1} (\frac{2s^3}{s^4-81})$

1. hartnn

i like Laplace

2. RolyPoly

$L^{-1} (\frac{2s^3}{s^2-81})=L^{-1} (2s+\frac{81}{s-9}+\frac{81}{s+9})$

3. RolyPoly

I don't like Laplace /_\

4. hartnn

i assume, thats correct, so whats the problem ?

5. RolyPoly

$L^{-1}(2s)=trouble$ Btw.. I... suddenly... discovered that... I read the problem wrong :\

6. RolyPoly

But how to find $$L^{-1}(2s)$$?

7. RolyPoly

For the correct question in the problem set: $L^{-1} (\frac{2s^3}{s^4-81})$$=L^{-1} (\frac{2s^3}{s^4-81})$$=L^{-1} (\frac{s}{s^2+9}+\frac{1}{2(s-3)}+\frac{1}{2(s+3)})$$=cos(3t)+cosh(3t)$

8. hartnn

sorry, my computer restarted.... to get L^{-1} (2s), u just replace 's' by 2s ....

9. RolyPoly

L^{-1} (s) also looks weird to me... Usually, it's a/s^n which I can do the inverse easily (easier, I mean)..

10. hartnn

ohh...i read that wrong .. u know whats L^{-1} s ?

11. hartnn

its $$\delta'(t)$$ so, $$L^{-1}(2s) = 2\delta'(t)$$

12. RolyPoly

What is $$\delta'(t)$$?

13. hartnn

u know what is $$\delta(t) ?$$

14. hartnn

Dirac delta function.. and ' means its derivative

15. RolyPoly

I.. don't remember I've learnt such function...

16. hartnn

really ? http://en.wikipedia.org/wiki/Dirac_delta_function 0 everywhere except origin.....like an impulse.

17. RolyPoly

I think I've only learnt int. from 0 to infty and from s to infty case, not the -ve infty to +ve infty... Thanks for introducing a new friend to me though :)

18. hartnn

hmm... welcome ^_^

19. RolyPoly

I want to get back my words. I don't know the name of this new friend, but he's just an old friend of mine :'( I'm sorry!!