Question

Find the laplace transform of f(t) = cos(wt) using direct integration.

Thanks guys! Just confused on what to do when using integration by parts, since we have two continious functions of t. >>> exp(-st) and cos(wt) <<<< we constantly need to use integration by parts and it's confusing me! I've read up on Eulers Identity, but i'm not sure how to actually apply it.

Answer 1

you decompose coswt into e^jwt+e^-jwt/2 it will help you

Answer 2

So how did you actually get that?

Answer 3

m doing...

Answer 4

\[\int\limits_{0}^{\infty}(e ^{jwt}+e ^{-jet})e ^{-st}dt/2\]=\[0.5[e ^{jwt-st}]/(jwt-st)-[e ^{-jwt-st}]/(jwt+st)|_{0}^{\infty}\]
1/2(jw+s)+(1/2(s-jw))=s/(s^2+w^2)

Answer 5

Yep I understand all that.. It's just why did you change cos(wt) to the (e^jwt+e^−jwt)

Answer 6

/2

Answer 7

ggabnore are u there?

Answer 8

yes

Answer 9

the decomposition of coswt comes from Eular's formula.

Answer 10

e^(jwt) = cos(wt) + jsin(wt), j=√(-1)

thats euler identity, how does it become... cos(wt) = e(jwt) + e(-jwt)

Answer 11

e^(-jwt)=cos(-wt)+jsin(-wt)
=coswt-jsinwt

add e^(jwt) and e^(-jwt) then sinwt cancels so you get only 2coswt

Answer 12

OH I seee. makes sense.. Thanks alot!