## ragman Group Title find inverse laplace transform of F(s)= (s^2+2s+5/(s^2(s+1)) one year ago one year ago

1. Skaematik Group Title

note

2. ragman Group Title

'note' sorry this is my first time using this what do you mean by that?

3. Skaematik Group Title

Im just bookmarking this question so that I can return to it later. :D Id want to know the answer too

4. ragman Group Title

oh ok sounds good thanks

5. lgbasallote Group Title

your question is $\huge \mathcal L ^{-1} \left \{ s^2 + 2s + \frac 5{s^2(s+1)}\right \}$

6. lgbasallote Group Title

??

7. lgbasallote Group Title

@ragman you there?

8. ragman Group Title

hey sorry about the late reply but my question is actually (s^2+22+5) / (s^2(s+1) sorry i forgot the other )

9. ragman Group Title

@lgbasallote

10. lgbasallote Group Title

uhh s^2 + 22 + 5??

11. ragman Group Title

dang i keep doing typos 2s not 22 so yeah its (s^2+2s+5)

12. lgbasallote Group Title

so.. $\huge \mathcal L ^{-1} \left \{ \frac{s^2 + 2s + 5}{s^2(s+1)} \right \}$

13. ragman Group Title

yup perfect

14. hartnn Group Title

can u do partial fractions ??

15. ragman Group Title

@hartnn yeah thats what i was doing but for some reason i could figure out the other two variable maybe im solving it incorrectly but i got -3 for A and 5 for B

16. lgbasallote Group Title

where's C?

17. hartnn Group Title

those are correct, so u need only C right ? where u took C above s+1

18. lgbasallote Group Title

your P.F. should be $\huge \frac As + \frac B{s^2} + \frac C{s+1}$

19. lgbasallote Group Title

so you have $\implies As(s+1) + B(s+1) + Cs^2 = s^2 + 2s + 5$

20. ragman Group Title

oh ok so thats where i messed up i thought that where C is it should be (Cs+D) so i was trying to solve for both of those variables

21. hartnn Group Title

nopes only C, if it were s^2+1 u would have taken Cx+D

22. hartnn Group Title

so i think u can get C now, right?

23. ragman Group Title

oh i see now and yeah i believe i can get C now trying it right now

24. lgbasallote Group Title

i think it will change your A value too

25. lgbasallote Group Title

so you best check

26. hartnn Group Title

great tell us what u get C as....we all will verify that. A is correct.

27. lgbasallote Group Title

nope nevermind..it stays the same

28. ragman Group Title

ok sounds good got B=5 finding A now

29. ragman Group Title

A=-3 and C=4 is that what you guys got?

30. hartnn Group Title

yup, same.Good work.

31. lgbasallote Group Title

A =-3?

32. lgbasallote Group Title

yeah that's right

33. ragman Group Title

ok cool i was about to write out how i got it lol

34. lgbasallote Group Title

everything's right

35. ragman Group Title

and now i just plug back all the variables right

36. hartnn Group Title

yup, and use inverse laplace formulas.

37. lgbasallote Group Title

yep find $\huge \mathcal L ^{-1} \left \{ -\frac 3s + \frac 5s + \frac 4{s+1} \right \}$

38. lgbasallote Group Title

uhh that should be 5/s^2

39. ragman Group Title

ok sorry im just learning this but how do you go about doing that im trying to find the L^-1 formula but my notes arent really helping

40. lgbasallote Group Title

here's a hint: $\huge \mathcal L \{ a \} = \frac as$ $\huge \mathcal L \{ t^n\} = \frac{n!}{s^{n+1}}$ $\huge \mathcal L \{e^{at} \} = \frac{a}{s -a}$ does that help?

41. lgbasallote Group Title

uhhh wait... wrong formula for last one

42. lgbasallote Group Title

$\huge \mathcal L \{e^{at} \} = \frac{1}{s-a}$ better

43. ragman Group Title

yes thats very helpful but im getting confused with what n should be in the middle equations

44. lgbasallote Group Title

n is the exponent

45. ragman Group Title

so it would be 2?

46. lgbasallote Group Title

for example: $\huge \mathcal L \{ t^2 \} = \frac{2!}{s^{2+1}} \implies \frac{2}{s^3}$

47. ragman Group Title

thats whats a lil confusing to me because on the denominator it would have to be n=1 so that it would equal s^2 but on the numerator 1! equals 1 right ?

48. hartnn Group Title

yes thats true, so u will have 5t^1= 5t ....isn't it ? u can verify that u should get final answer as 5t-3+4e^(-t) did u get that?

49. ragman Group Title

yup thats what i got thanks

50. hartnn Group Title

welcome :)