Question

Find f(t).
f(t)= L−¹{4s/(s−3)²​}
f(t) = ___

Answer 1

To find f(t), we need to find the inverse Laplace transform of 4s/(s-3)^2. The inverse Laplace transform of s/(s-3)^2 is e^(3t). Therefore, f(t) = 4e^(3t).

Step-by-step explanation:

To find f(t), we need to find the inverse Laplace transform of 4s/(s-3)^2. The Laplace transform of a function f(t) is defined as F(s) and the inverse Laplace transform is given by L^-1{F(s)}. In this case, we have f(t) = L^-1{4s/(s-3)^2}.

Using the properties of Laplace transforms, we can rewrite the expression as f(t) = 4L^-1{s/(s-3)^2}. The inverse Laplace transform of s/(s-3)^2 is e^(3t). Therefore, the final expression for f(t) is f(t) = 4e^(3t).