Question

Find Laplace transform of L[3+t]

Answer 1

Answer:

we write cos(4t) = f(t), say. now if l(f(t)) = f(s), then, by theorem on derivatives of laplace transforms, we have l(t.f(t)) = -f'(s), where the ' denotes derivative with respect to s. we know that

l(cos(4t)) = s/(s^2+16). therefore in view of the above theorem,

(s^2–16)/(s^2 +16)^2. similarly applying the theorem twice more we get l(t^3.cos(4t)).