Laplace Transform 3 (L{sin(at)})

Laplace Transform of sin(at) (part 1)

Category:

Education

Tags:

• laplace
• transform

[khanacademy]

Depends on what you pick for u and v. I rederive the formula from the product rule everytime (it's the only way you'll remember it 15 years after taking calculus)

[sikory]

I saw an interesting and much faster way to derive this by using the backwards Euler Formula: sin(at)=(exp(iat)-exp(-iat))/2­i

or by taking the imaginary part of the Laplace transform of exp(iat)

[youngspen]

is this right?: i let u = e^-st and dv = sin at

then differentiate u for du = -1/s e^-st

then integrate dv for v = -a cos at

i dont get how you got (a cos at) as positive.

[ahmoodloova]

@sadga03

haha hate it too but look to this simple method=

we all know--> cos t=1/2[e^jt+e^-jt] ,we can use that to solve

so it will be F(s)= (integration of cos t .e^-st)=

integration of (1/2[e^jt+e^-jt].e^-st)=

i/2[(1/s-j)=(1/s+j)]...=s/s^2+­1^2

its much easier than all of that ^_^

[sadga03]

that's y i hate integration by parts... it make me confius... huh... =.="

[SeanRVCA]

I FREAKIN hate integration by parts!!

[Bisharpual]

9:25 "...cos at, now i wanna make sure i dont make any careless mistakes *checks intently* ... ok so now there's a minus sign *scratches out t thinking its a + sign*" lol

[9588alamALI]

wow ! great videos ! pure concept building

[curiosityuniversal]

Whoa infinite loop!!!... going to watch the next video to see how you get out of this one xD