Question

how to compute the following inverse Laplace Transform? (L^-1){1-(e^-s)/s(1+(e^-s)

Answer 1

\[ L^{-1}\{\frac{1-e^-s}{s(1+e^-s)}\}\]

Answer 2

it looks like its related to the shifts since it still retains the e parts

Answer 3

correct, its number 3 on the picture I provided, I didnt notice until now the attach document tab

Answer 4

partial it up for starters is my first guess

Answer 5

to dbl chk your efforts when your done, you can always try this

http://www.wolframalpha.com/input/?i=laplace+inverse

Answer 6

we learned about the laplace recently, but we never got to shifts

Answer 7

yeah, we learned the whole chapter in two bloody lectures.

Answer 8

the wolf is acting up on this one .....

Answer 9

How would you check using the wolfram link, it just gives me the original

Answer 10

hey amistre would not we need to break in partial fraction, yes indeed we need to i guess

Answer 11

http://tutorial.math.lamar.edu/Classes/DE/StepFunctions.aspx

if youve already been exposed to it, this might be useful. I find that this site gives some clear explanations most of the time

Answer 12

also a useful page
http://tutorial.math.lamar.edu/Classes/DE/InverseTransforms.aspx

Answer 13

I have that exact link already open lol

Answer 14

dark go have you tried it with partial fractions?

Answer 15

I have not, we didn't really go into detail in our lectures so much, we just pretty much went through the properties not so much how to solve them

Answer 16

wait lemme see if i can do it, and which year in college u r>

Answer 17

Sophmore, senior by credits.

Answer 18

\[\frac{-(e^{-s}+1)}{s(1+e^{-s})}\]\[\frac{e^{-s}-1+1-1}{-s(e^{-s}+1)}\to\ \frac{(e^{-s}+1)}{-s(e^{-s}+1)}+\frac{-2}{s(e^{-s}+1)} \]

Answer 19

dropped a negative; forget the -2; its just 2

Answer 20

how do you do the second guy?

Answer 21

the first Ls over to -1 i believe; the second one tho .... hmmm

Answer 22

I have never seen e^-s in the denom before

Answer 23

how can we remove it then?

Answer 24

hmm amistre for the first part you are correct , and yes @TuringTest i am all stuck in resolving e^-s , idk where the hell it come from

Answer 25

I tried multiplying by e^s/e^s and (1+e^(-s))/(1+e^(-s))
and either way I wind up with e^(+/-s) in the denom, which I don't know how to deal with

Answer 26

if the e^-s wasnt there ... what would we get?

Answer 27

perhaps our Professor meant to have e^-st instead? e^-st is all over our notes

Answer 28

1/s lol

Answer 29

amistre then it would have been a kids prob :P

Answer 30

:) im wondering because I did a shift the other day and the only diff between my efforts and the actual results was that my answer required a multiplication by e^as

Answer 31

so im wondering if we divide out the e^-s what it turns to

Answer 32

I tried that, but how can we keep it out of the denominator?

Answer 33

ok wait solve this in partial fraction by taking out value of A and B

A/(s) + B/(e^-s+1)=2

Answer 34

A turns out to be 1, find for B

Answer 35

if we find B then our laplace is resolved

Answer 36

when s=inf .... B goes to 0

Answer 37

yup , true , hence we are left with only laplace of -(1/s) that is -1

Answer 38

i think problem is done !

Answer 39

@DarKGo its done , the final answer is just -2 Lol

Answer 40

are we sure about that?

Answer 41

its not done until you prove it with something more substantial than "i say so" lol

Answer 42

I don't think sooo

Answer 43

im i guess, because i broke into partial fractions, and this is a valid method to break into partial and solve

Answer 44

A/(s) + B/(e^-s+1)=2
is not the right decomposition

Answer 45

the start is from a piecewise function; which means we have to end up with a piecewise answer

Answer 46

..I think
I need more coffee :)

Answer 47

@TuringTest test then how else can we break into partial fractions?

Answer 48

i do believe -1 is one of the pieces, but i cant determine the interval

Answer 49

where did the 2 come from
?

Answer 50

the way amistre simplified it , we got -2/{(s)(e^-s+1)}

Answer 51

\[\frac{2}{s(e^{-s}+1)}\]
would be the second part of the doodad i did upstaris

Answer 52

oh I see you just did the second part

Answer 53

yes , because first part is piece of cake

Answer 54

soo tell is it right to break in the way i did , cause i cant see any other way now ,@amistre64 @TuringTest ?

Answer 55

lets try to reverse engineer some of this

suppose we wanted the laplace of the function

f(x) = 1 from 0 to 4
=-1 from 4 to inf

what would we get?

Answer 56

...need more coffee to verify this....

Answer 57

amistre i know the reverse thing wont prove, but the way you simplified this prob ,leave the option of partial fractions only , or if you dont wanna do that find a way to counter (e^-s+1)

Answer 58

so has an answer been agreed upon or still up in the air?

Answer 59

in the air Lol

Answer 60

I'd say we're still floating around, yeah

Answer 61

@Mr.Math Laplace transform help?

Answer 62

hanging around in the air , with lots of clouds so we unable to see any direction :P

Answer 63

inshAllah someone else can provide insight lol.

Answer 64

@dumbcow @satellite73 plz help

Answer 65

i can get my example up to \[\frac{-2(e^{-8s}-e^{-4s}+\frac{1}{4})}{s(e^{-s}-\frac{1}{2})}\]

Answer 66

can we factor your top to a difference of squares?

Answer 67

I tried that too, it didn't pay off for me. good luck

Answer 68

1
---------
1+e^s ) 1-e^s
(1+e^s)
-------
-2e^s

hmm

Answer 69

\[\frac{1-\frac{2}{1+e^{-s}}}{s}\to\ \frac{1}{s}+\frac{-2}{s(1+e^{-s})}\]
gets us back to there lol

Answer 70

wolf does not want to do that second term
http://www.wolframalpha.com/input/?i=inverse%20laplace%20-2%2F(s(1%2Be%5E(-s))&t=crmtb01

Answer 71

Loool nice work :P

Answer 72

doesnt the step thing have something to do with F(s)/G(s) ??

Answer 73

im hallucinating so bad right now from sleep deprivation lol

Answer 74

I am beginning to suspect something is wrong with this problem

Answer 75

this we can agree upon Lol

Answer 76

perhaps this might be of some help? And i dont think the problem is wrong its in both the differential equations and boundary value problems 4th edition textbook and our professors own textbook

Answer 77

ok, then we are probably just missing something....

Answer 78

http://www.physicsforums.com/showthread.php?t=220407 I forgot to put that in my last reply, maybe this might be of some use

Answer 79

omg wait i guess i have some idea, @TuringTest rationalize the e^-s+1

Answer 80

tried it, got what amistre got
go ahead and see if you get something different

Answer 81

ahhh ok

Answer 82

i can get it to go complex lol. but im at a stand still on it without knowing the step stuff in and out

Answer 83

tell your teacher to solve it ;)

Answer 84

its homework assignment due in a few hours

Answer 85

im sure youre allowed to not know somethings ....

Answer 86

nope, homework is worth 50%

Answer 87

well that sucks

Answer 88

sadness

Answer 89

well dark, i have yet to see you contribute anything substantive to the conversation. What do you know that you can bring to the table?

Answer 90

I don't know much honestly, this is going to be discussed in today's lecture but he includes it in the homework anyway.

Answer 91

i havent been able to drum up anything useful ... i feel that it has some trig involved; and that the intervals in question are from 0 to 1 and 1 to inf ..... but other than that im at a loss still