Question

HI ... PLEASE HELP

Answer 1

laplace transform of
\(\large f(t) = e^{-at} \cos (w)t\)

Answer 2

@dan815 ... seeing as ur indoors... lil help? ;P

Answer 3

hey man, u any good at these...? @jim_thompson5910

Answer 4

got a sec bro @ganeshie8 ?

Answer 5

@iambatman ...?

Answer 6

what's this o-o Calc

Answer 7

yep, crazy calculus

Answer 8

haha, I've never took "Crazy calc" before

Answer 9

its hard... would not recommend :(

Answer 10

Hmm, Let's see if I can generate an solution :P

Answer 11

hey i think writing cos(wt) using reverse euler identity and plugging the whole thing into laplace integral should be easy right ?

Answer 12

cosx = e^x + e^-x / 2

Answer 13

... is this right:
a+s/ (a+s)^2 + w ?

Answer 14

a+s/ (a+s)^2 + w^2

right ?

Answer 15

lol simply using the exponential shift wud work too...

Answer 16

ah, yep, sorry, forgot the w^2... my bad

Answer 17

cos(wt) ---> s / s^2+w^2

e^(-at)cos(wt) ----> s+a / (s+a)^2 + w^2

Answer 18

so ur just subbing (s+a) in place of s for those... yeah?

Answer 19

yeah

Answer 20

because L [e^-at] = 1/s+a...?

Answer 21

nope

Answer 22

darn...

Answer 23

because of exponential shift rule :

e^at * f(t) ----> F(s-a)

Answer 24

ahhhh... ok

Answer 25

multiplying a function by `e^(at)` shifts its laplace tranform by `a` units

Answer 26

with u now, cheers man!

Answer 27

np :)

watch this when ur free
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-19-introduction-to-the-laplace-transform/

Answer 28

will do... exam tomorrow, so will watch in hols, only 1 q on this tho

Answer 29

wow ! i can see you're fully ready for the exam :) good luck !!

Answer 30

cheers man