Laplace Transformations

[NozlerAtClemson]

I am trying to solve: t y'' - t y' + y=2, y(0)=2, y'(0)=-1
I get stuck at:
d/ds(((s-1)^2)Y)=(2(s-1)^2)/s^2

 

[NikPreviousAcct]

:Q :| OW, dammit, now I have a headache!



j/k - btw, is this calc or physics or something?

nik

 

[Chaotic42]

Originally posted by: ffmcobalt
:Q :| OW, dammit, now I have a headache!



j/k - btw, is this calc or physics or something?

nik

Let's just say they don't cover it until Chapter 11 of my post-graduate Calc book.

 

[CrazyDe1]

haha...I hate laplace transforms

 

[rudder]

screw it, go get a beer.

 

[NikPreviousAcct]

Originally posted by: rudder
screw it, go get a beer.

Hell yeah

 

[EvilYoda]

damn......if I wasn't too lazy to write that down, I might remember something, but sorries. After you get it once or twice, it should get pretty easy, so at leas tyou have something to look forward to

 

[CrazyDe1]

Is this a differential equations class or a circuits or signal processing class?

 

[DanTMWTMP]

damn wait till u do convolutions....this is from EE eh?...i hated hated that...well, it beats doing n-th order calculations which took up 5 pages for one problems........well, wait till u do fourier transform...lotsa easier...it only gets easier after laplace.....


well for that use the identity...arg forgot it...i don't have my book w/ me...but it's in the book...u can find laplace identities online also...just do a google search...some .edu site might have it.....good luck dude

 

[xyion]

Laplace isnt so bad. now, deriving Laplace eq, thats not cool at all.

But sorry, I cant help you with your question.

 

[AvesPKS]

Originally posted by: DanTMWTMP
damn wait till u do convolutions....this is from EE eh?...i hated hated that...well, it beats doing n-th order calculations which took up 5 pages for one problems........well, wait till u do fourier transform...lotsa easier...it only gets easier after laplace.....


well for that use the identity...arg forgot it...i don't have my book w/ me...but it's in the book...u can find laplace identities online also...just do a google search...some .edu site might have it.....good luck dude

What? Are you insane? LaPlace is way easier than Fourier. Fourier transforms and series suck big time. And convolution is easy, too. Our teacher told us that if there was one thing we'd learn in this class, it'd be convolution. Discrete convolution can be a little tricky, I'll give you that, but continuous convolution is super easy. Especially graphical methods.

 

[NozlerAtClemson]

Calc 4, I am done with math after this class; Maple says the answer is -t+2 but I can't get anywhere near that.

 

[SyahM]

If i didnt screw up my Signals and Systems class I wud be able to answer that with ease, but too bad, i messed up and switch my major to finance '
Good luck!

 

[Ameesh]

Originally posted by: Chaotic42

Originally posted by: ffmcobalt
:Q :| OW, dammit, now I have a headache!



j/k - btw, is this calc or physics or something?

nik

Let's just say they don't cover it until Chapter 11 of my post-graduate Calc book.

are you kidding?! this is undergrad calc.

 

[Anubis]

ahh maple is my god.

anyway laplace transforms are NO WHERE NEAR as hard as Fourierr transfoems and series. we did thoes last year in 2 different physics classes. Waves, and then in Theroticial physics. man they sucked

electrodynamics is SO easy compaired to that.

we had a fourier sin series in excell to fit a function to a line and it was so big it was killing Dual G4 macs and some SUN systems we had it on. finally it to work but had to change things 1 at a time. tried to do a bunch and BOOM comp crash

 

[ArmenK]

Originally posted by: NozlerAtClemson
I am trying to solve: t y'' - t y' + y=2, y(0)=2, y'(0)=-1
I get stuck at:
d/ds(((s-1)^2)Y)=(2(s-1)^2)/s^2

-d[s^2Y(s)-sy(0)-y'(0)]/ds + d[sY(s) - y(0)]/ds + Y(s) = 2/s
-d[s^2Y(s)-2s+1]/ds + d[sY(s) - 2]/ds + Y(s) = 2/s

-d[s^2Y(s)]/ds + 2 + d[sY(s)]/ds + Y(s) = 2/s
-2sY(s) - s^2Y'(s) + Y(s) + sY'(s) + Y(s) = 2/s - 2
Y(s)(2-2s) + Y'(s)(s - s^2) = (2-2s)/s
2Y(s)(1-s) + sY'(s)(1 - s) = 2(1-s)/s
2Y(s) + sY'(s) = 2/s


ack, i give up, dont have enough time to solve it

 

[Chaotic42]

Originally posted by: Ameesh

Originally posted by: Chaotic42

Originally posted by: ffmcobalt
:Q :| OW, dammit, now I have a headache!



j/k - btw, is this calc or physics or something?

nik

Let's just say they don't cover it until Chapter 11 of my post-graduate Calc book.

are you kidding?! this is undergrad calc.

Actually I mistyped! I meant to say Advanced Calc (sorry, I was really out of it earlier)

 

[DanTMWTMP]

Originally posted by: AvesPKS

Originally posted by: DanTMWTMP
damn wait till u do convolutions....this is from EE eh?...i hated hated that...well, it beats doing n-th order calculations which took up 5 pages for one problems........well, wait till u do fourier transform...lotsa easier...it only gets easier after laplace.....


well for that use the identity...arg forgot it...i don't have my book w/ me...but it's in the book...u can find laplace identities online also...just do a google search...some .edu site might have it.....good luck dude

What? Are you insane? LaPlace is way easier than Fourier. Fourier transforms and series suck big time. And convolution is easy, too. Our teacher told us that if there was one thing we'd learn in this class, it'd be convolution. Discrete convolution can be a little tricky, I'll give you that, but continuous convolution is super easy. Especially graphical methods.

aha of course continious convolution is super easy...but my class...they concentrate all on discrete..well, converting btwn the two isn't that all bad.....wut!! fourier is easier! u gotta be insane..ahah maybe it's cuz we had to derive the laplace every time....and probably depends on professor.....graphical convolution = ayayayayy! ....but doing it all via formula = i hate.....i probably had a bad professor...booo aha

 

[eLiu]

Originally posted by: NozlerAtClemson
I am trying to solve: t y'' - t y' + y=2, y(0)=2, y'(0)=-1
I get stuck at:
d/ds(((s-1)^2)Y)=(2(s-1)^2)/s^2

Laplace...i learn that next semester in partial difeq; it's in a book I have, but the hell if i can make any sense out of it now

 

[Random Variable]

We just started learning about Laplace transformations on Wednesday. Ask me again in a couple weeks.

 

[Eric321]

Originally posted by: NozlerAtClemson
I am trying to solve: t y'' - t y' + y=2, y(0)=2, y'(0)=-1
I get stuck at:
d/ds(((s-1)^2)Y)=(2(s-1)^2)/s^2

Am I missing something? What happend to "t"?

 

[AvesPKS]

Originally posted by: DanTMWTMP

Originally posted by: AvesPKS

Originally posted by: DanTMWTMP
damn wait till u do convolutions....this is from EE eh?...i hated hated that...well, it beats doing n-th order calculations which took up 5 pages for one problems........well, wait till u do fourier transform...lotsa easier...it only gets easier after laplace.....


well for that use the identity...arg forgot it...i don't have my book w/ me...but it's in the book...u can find laplace identities online also...just do a google search...some .edu site might have it.....good luck dude

What? Are you insane? LaPlace is way easier than Fourier. Fourier transforms and series suck big time. And convolution is easy, too. Our teacher told us that if there was one thing we'd learn in this class, it'd be convolution. Discrete convolution can be a little tricky, I'll give you that, but continuous convolution is super easy. Especially graphical methods.

aha of course continious convolution is super easy...but my class...they concentrate all on discrete..well, converting btwn the two isn't that all bad.....wut!! fourier is easier! u gotta be insane..ahah maybe it's cuz we had to derive the laplace every time....and probably depends on professor.....graphical convolution = ayayayayy! ....but doing it all via formula = i hate.....i probably had a bad professor...booo aha

We don't have to derive the LT's...just use the charts. And he actually took points off on the test if we integrated on convolution. He made us do it graphically.

 

[pillage2001]

Doing a DEQ laplace Q eh?? can't help. Totally forgotten all I had done a year or so before.

 

[TCPpacket]

Originally posted by: ArmenK

Originally posted by: NozlerAtClemson
I am trying to solve: t y'' - t y' + y=2, y(0)=2, y'(0)=-1
I get stuck at:
d/ds(((s-1)^2)Y)=(2(s-1)^2)/s^2

-d[s^2Y(s)-sy(0)-y'(0)]/ds + d[sY(s) - y(0)]/ds + Y(s) = 2/s
-d[s^2Y(s)-2s+1]/ds + d[sY(s) - 2]/ds + Y(s) = 2/s

-d[s^2Y(s)]/ds + 2 + d[sY(s)]/ds + Y(s) = 2/s
-2sY(s) - s^2Y'(s) + Y(s) + sY'(s) + Y(s) = 2/s - 2
Y(s)(2-2s) + Y'(s)(s - s^2) = (2-2s)/s
2Y(s)(1-s) + sY'(s)(1 - s) = 2(1-s)/s
2Y(s) + sY'(s) = 2/s


ack, i give up, dont have enough time to solve it

For the Laplace equation, i got
L[dy(t)/dt] = sY(s) - y(0) = sY(s) - 2
L[d^2y(t)/dt^2] = s^2Y(s) - 2s + 1

so the original equation becomes:
s^2Y(s) - 2s + 1 - sY(s) + 2 + Y(s) = 2/s

rearranging for Y(s), you get:
Y(s) = (2/s + 2s - 3) / (s^2 - s + 1)

do a partial fraction expansion on this equation and then do an inverse Laplace on each partial fraction to get the answer.

hope this helps (hopefully i did it right, hehe)

 

[Triumph]

laplace is AWESOME. they put you through a semester of solving differential equations by hand. then you get into system dynamics and they say, "Here is the easy, algabraic method." THANK YOU!