Question

would
\[LT \left[ tu(t-30) \right]=\frac{ e ^{-30s} }{ s ^{2} }\]

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

Answer 1

we know that

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

Answer 2

just from laplace tables

Answer 3

ideas?

Answer 4

Have you tried going through the integration?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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?

Answer 11

do a change of variables

Answer 12

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

Answer 13

ohh yea neat

Answer 14

Thanks @dan815

Answer 15

yeah nah that drawing has confused me lel

Answer 16

lol

Answer 17

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

Answer 18

haha no joke i was gonna say

Answer 19

now u became the variable for laplace

Answer 20

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

Answer 21

could we just expand those brackets

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

and laplacing these would be the same...

Answer 26

where a=t-30

Answer 27

ohh something silly here oops

Answer 28

ont need to even worry about all this apprently

Answer 29

lel

Answer 30

this is U_c(t) by definition

Answer 31

yep

Answer 32

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'