anonymous
  • anonymous
would \[LT \left[ tu(t-30) \right]=\frac{ e ^{-30s} }{ s ^{2} }\] i'm not sure if applying the formula below would be right. \[LT \left[ u _{c}(t)f(t-c) \right]=e ^{-cs}F(s)\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
we know that \[LT \left[ u _{c}(t)=u(t-c) \right]=\frac{ e ^{-cs} }{ s }\]
anonymous
  • anonymous
just from laplace tables
anonymous
  • anonymous
ideas?

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anonymous
  • anonymous
Have you tried going through the integration?
anonymous
  • anonymous
im unsure how to do that when we are considering u(t-30)
anonymous
  • anonymous
Do you know how to work with the dirac delta function?
anonymous
  • 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
  • anonymous
like, i start with the integral definition, \[LT(f(t)=\int\limits_{0}^{\infty}e ^{-st}tu(t-30)dt\]
anonymous
  • 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
  • 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
  • dan815
do a change of variables
anonymous
  • anonymous
dv is the exponential and u is the t*u(t-30)
anonymous
  • anonymous
ohh yea neat
anonymous
  • anonymous
Thanks @dan815
anonymous
  • anonymous
yeah nah that drawing has confused me lel
dan815
  • dan815
lol
dan815
  • dan815
i realized using s for the different variable was bad idea lol
anonymous
  • anonymous
haha no joke i was gonna say
dan815
  • dan815
now u became the variable for laplace
dan815
  • dan815
lemme think so i wonder if we gotta add some extra stuff in for this shift
anonymous
  • anonymous
could we just expand those brackets
anonymous
  • anonymous
so instead of s lets use 'a' as our variable
anonymous
  • anonymous
(a+30)u(a)= au(a)+30u(a)
dan815
  • dan815
its best to jst graph this stuff so we know for sure we dont have anything funky going on
anonymous
  • anonymous
and laplacing these would be the same...
anonymous
  • anonymous
where a=t-30
dan815
  • dan815
ohh something silly here oops
dan815
  • dan815
ont need to even worry about all this apprently
anonymous
  • anonymous
lel
dan815
  • dan815
this is U_c(t) by definition
anonymous
  • anonymous
yep
anonymous
  • 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
  • dan815
|dw:1443326746594:dw|
dan815
  • dan815
i think what we did might be find, think abouut it like this, what is the laplace of this bottom graph
dan815
  • dan815
fine*
anonymous
  • anonymous
just a ramp function, shifted from the origin..
dan815
  • dan815
u_30(t) * ((t-30)+30)
dan815
  • 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
  • dan815
yay
dan815
  • dan815
|dw:1443326992420:dw|
dan815
  • dan815
|dw:1443327070058:dw|
dan815
  • dan815
this make sense?
dan815
  • dan815
|dw:1443327188716:dw|
anonymous
  • anonymous
with the first and second step |dw:1443327215719:dw|
dan815
  • dan815
ya?
anonymous
  • anonymous
should the first step be f(t-30)
dan815
  • dan815
no taht is what is figven
dan815
  • dan815
so i changed it to something that is f(t-30)
anonymous
  • anonymous
|dw:1443327270524:dw|
anonymous
  • anonymous
like what thats mean
dan815
  • dan815
(t)
anonymous
  • anonymous
oh yea ns
anonymous
  • anonymous
haha
anonymous
  • anonymous
yeap sweet as man, cheers!
dan815
  • dan815
ok baby
dan815
  • dan815
greetings from Canada xD
anonymous
  • anonymous
ur such a lad haha
dan815
  • dan815
lel
anonymous
  • anonymous
still havent moved ay
dan815
  • dan815
how r things down in australia these days
anonymous
  • anonymous
yea summer is coming, soo good. only like another 2 months then i'm in 4th yr.
dan815
  • dan815
truee yeee
anonymous
  • anonymous
hopefully get a job and i'll be done yesss
dan815
  • dan815
good luck :)
anonymous
  • anonymous
cheers man, hbu?
dan815
  • dan815
same story pretty much, gotta do capstone next year and land jobs
anonymous
  • anonymous
wuts capstone?
dan815
  • dan815
itsd like this project every engineer has to do for final year, i think u too
anonymous
  • anonymous
oh like research project
dan815
  • dan815
yeah
anonymous
  • anonymous
yeah that will be aids
dan815
  • 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
  • anonymous
yeah thats our research project haha mine will focus more on mining but not sure what yet
anonymous
  • anonymous
yolo
dan815
  • dan815
oh you decided already xD i still got no idea
dan815
  • dan815
ill probably do some detection stuff i just wanna write code and make my partners do the more circuit stuff
anonymous
  • 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
  • dan815
cool
dan815
  • dan815
what kind engineering is that?
anonymous
  • anonymous
chemical eng. so gai
dan815
  • dan815
oooo
dan815
  • dan815
chemistry is too hard -.-
anonymous
  • anonymous
haha its pretty hectic but what i enjoy so its chill as.
dan815
  • 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
  • anonymous
too many people will fail hahaha
anonymous
  • anonymous
lots of science students aren't well educated in math anyway
anonymous
  • 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
  • dan815
alright take care!!

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