find the laplace transform for

Q : cos(ωt+k)
A : (s*cos(k)-ω*sin(k))/(s^2+k^2)

lot's of questions are coming , ... what are the steps .

 

L{e^(3a-2b)} = (e^3a)/(s+2b)

L{sin(t)*cos(t)} = 1/s^2+4

 

find the laplace transform for

Q : cos(ωt+k)
A : (s*cos(k)-ω*sin(k))/(s^2+k^2)

lot's of questions are coming , ... what are the steps .

f(t)=cos(ωt+k) is one of the standard forms and is usually given in any comprehensive table of Laplace Transform pairs.

If you want to go through the derivation you can attempt it yourself or look it up in a maths text book - you could probably Google it and get the derivation.

As a starting practice question you could try deriving the Laplace transform for the simpler case of f(t)=cos(ωt) which is a reasonable challenge for the beginner. How's your integration skill these days?

 

L{e^(3a-2b)} = (e^3a)/(s+2b)

L{sin(t)*cos(t)} = 1/s^2+4

May I suggest you restrict yourself to the one question (perhaps with some supplementary discussion on that question) rather than stacking up more new questions one after the other in the same thread. This won't get you any favorable attention - rather it's more likely to alienate people.

Also you should make an earnest attempt to answer the questions yourself - this isn't a free on-line homework service.

 

youtube has a lot of good videos that show you how to derive them.