would
\[LT \left[ tu(t-30) \right]=\frac{ e ^{-30s} }{ s ^{2} }\]
i'm not sure if applying the formula below would be right.
\[LT \left[ u _{c}(t)f(t-c) \right]=e ^{-cs}F(s)\]

- anonymous

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- anonymous

we know that
\[LT \left[ u _{c}(t)=u(t-c) \right]=\frac{ e ^{-cs} }{ s }\]

- anonymous

just from laplace tables

- anonymous

ideas?

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## More answers

- anonymous

Have you tried going through the integration?

- anonymous

im unsure how to do that when we are considering u(t-30)

- anonymous

Do you know how to work with the dirac delta function?

- anonymous

not really, we just have a table of lapalce transforms used to help us in process control. my laplace transform is limited considering we weren't taught this in engineering maths yet it has come up in a third year topic which applies laplace transforms

- anonymous

like, i start with the integral definition,
\[LT(f(t)=\int\limits_{0}^{\infty}e ^{-st}tu(t-30)dt\]

- anonymous

and try integration by parts...but i'm stuck with the t*u(t-30) bit, with applying the product rule on it

- anonymous

Ok, so if you are using integration by parts, then you are considering this integral of the from\[\int\limits_{}^{}u dv = uv - \int\limits_{}^{}v du\]. What are you using as your u and your dv?

- dan815

do a change of variables

- anonymous

dv is the exponential and u is the t*u(t-30)

- anonymous

ohh yea neat

- anonymous

Thanks @dan815

- anonymous

yeah nah that drawing has confused me lel

- dan815

lol

- dan815

i realized using s for the different variable was bad idea lol

- anonymous

haha no joke i was gonna say

- dan815

now u became the variable for laplace

- dan815

lemme think so i wonder if we gotta add some extra stuff in for this shift

- anonymous

could we just expand those brackets

- anonymous

so instead of s lets use 'a' as our variable

- anonymous

(a+30)u(a)= au(a)+30u(a)

- dan815

its best to jst graph this stuff so we know for sure we dont have anything funky going on

- anonymous

and laplacing these would be the same...

- anonymous

where a=t-30

- dan815

ohh something silly here oops

- dan815

ont need to even worry about all this apprently

- anonymous

lel

- dan815

this is U_c(t) by definition

- anonymous

yep

- anonymous

but we can't use the formula thats on the top page cause it involves f(t-c) so here c=0 for the function f, but 30 for variable 'u'

- dan815

|dw:1443326746594:dw|

- dan815

i think what we did might be find, think abouut it like this, what is the laplace of this bottom graph

- dan815

fine*

- anonymous

just a ramp function, shifted from the origin..

- dan815

u_30(t) * ((t-30)+30)

- dan815

with this trick now we have a new function f(t)=t+30
and f(t-c)=f(t-30)=(t-30)+30

- dan815

yay

- dan815

|dw:1443326992420:dw|

- dan815

|dw:1443327070058:dw|

- dan815

this make sense?

- dan815

|dw:1443327188716:dw|

- anonymous

with the first and second step |dw:1443327215719:dw|

- dan815

ya?

- anonymous

should the first step be f(t-30)

- dan815

no taht is what is figven

- dan815

so i changed it to something that is f(t-30)

- anonymous

|dw:1443327270524:dw|

- anonymous

like what thats mean

- dan815

(t)

- anonymous

oh yea ns

- anonymous

haha

- anonymous

yeap sweet as man, cheers!

- dan815

ok baby

- dan815

greetings from Canada xD

- anonymous

ur such a lad haha

- dan815

lel

- anonymous

still havent moved ay

- dan815

how r things down in australia these days

- anonymous

yea summer is coming, soo good. only like another 2 months then i'm in 4th yr.

- dan815

truee yeee

- anonymous

hopefully get a job and i'll be done yesss

- dan815

good luck :)

- anonymous

cheers man, hbu?

- dan815

same story pretty much, gotta do capstone next year and land jobs

- anonymous

wuts capstone?

- dan815

itsd like this project every engineer has to do for final year, i think u too

- anonymous

oh like research project

- dan815

yeah

- anonymous

yeah that will be aids

- dan815

yeah its just htis one course that runs for the whole year and u have to work on it in your own time

- anonymous

yeah thats our research project haha
mine will focus more on mining but not sure what yet

- anonymous

yolo

- dan815

oh you decided already xD i still got no idea

- dan815

ill probably do some detection stuff i just wanna write code and make my partners do the more circuit stuff

- anonymous

my degree is focused in minerals processing/mining so its like i am forced to do something mining like haah
yeah writing code sounds fun hahaha

- dan815

cool

- dan815

what kind engineering is that?

- anonymous

chemical eng. so gai

- dan815

oooo

- dan815

chemistry is too hard -.-

- anonymous

haha its pretty hectic but what i enjoy so its chill as.

- dan815

u gotta actually learn like a lot of math to do real chem, but they dont teach all that math in a chem degree

- anonymous

too many people will fail hahaha

- anonymous

lots of science students aren't well educated in math anyway

- anonymous

but enough of me speaking, i need some lunch!
i'll let ya know how i go with this question after.
cheers mate. peace

- dan815

alright take care!!

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