What is the proof of this? Or rather, could somebody get me started and point me in the right direction for this?
Thanks! Any help is appreciated.
Wat the "TheEmptySet" has showed is perfectly right but i like to show the same proof in another way ...We know by theorem Laplace {{e^at} f(t)}=F(s-a)
Proof of the theorem:
We know L{f(t)}=Intergral 0-infinity ({e^-st} f(t) dt)=F(s)
Therefore Intergral {e^at f(t)} = Intergral 0-infinity ({e^-st}{e^at} f(t) dt)
=Intergral 0-infinity ({e^-(s-a)t} f(t) dt)
=F(s-a) {Reason:Since Intergral 0-infinity ({e^-st} f(t) dt)=F(s)}
Hence Laplace {{e^at} f(t)}=F(s-a)..
In the qn here in the place of f(t) we have coskt..
Therefore we know laplace {coskt}=s/(s^2-k^2) = F(s)
Therefore F(s-a)=(s-a)/{(s-a)^2-k^2}
I think ive done my best to make the script understandable..
If not im really sorry about the inconvenience..