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anonymous
 5 years ago
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.
anonymous
 5 years ago
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.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you decompose coswt into e^jwt+e^jwt/2 it will help you

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So how did you actually get that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\infty}(e ^{jwt}+e ^{jet})e ^{st}dt/2\]=\[0.5[e ^{jwtst}]/(jwtst)[e ^{jwtst}]/(jwt+st)_{0}^{\infty}\] 1/2(jw+s)+(1/2(sjw))=s/(s^2+w^2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yep I understand all that.. It's just why did you change cos(wt) to the (e^jwt+e^−jwt)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ggabnore are u there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the decomposition of coswt comes from Eular's formula.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0e^(jwt) = cos(wt) + jsin(wt), j=√(1) thats euler identity, how does it become... cos(wt) = e(jwt) + e(jwt)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0e^(jwt)=cos(wt)+jsin(wt) =coswtjsinwt add e^(jwt) and e^(jwt) then sinwt cancels so you get only 2coswt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OH I seee. makes sense.. Thanks alot!
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