what is the Laplace transform of e^4t(cos 2t) ?

Answer 1

since there is e^4t multiplied to cos(2t), there is s-shifting:
from e^4t, we know that a = 4,, we also know that L{cos 2t} = s/(s^2 + 4) , therefore:
L{e^4t(cos 2t)} = (s-a)/((s-a)^2 + 4) = (s-4)/((s-4)^2 + 4)

so there,, =)

Answer 2

thanks a bunch.