(b) F(s) = 3s+2 /s^2+2s+10

(c) F(s) = 1/ s^2+16

Solved Step by step with explanation. Find the time function corresponding.

Step 2: Express F(s) in partial fraction form.

F(s) = A/(s + 1) + B/(s + 5)

-1 = A (-1 + 5) + B(-1 + 1)

-1 = 4A

B = 5/4

So, F(s) can be written as:

We can now consult a Laplace transform table to find the inverse Laplace transform of each term.

L^-1 {(-1/4)/ (s + 1)} = -1/4 * e^(-t)

L^-1 {F(s)} = L^-1 {(3s + 2)/(s^2 + 2s + 10)}

Again, we'll consult a Laplace transform table to find the inverse Laplace transform.

(c) To find the time function corresponding to the Laplace transform F(s) = 1/(s^2 + 16), we'll use the inverse Laplace transform directly.

L^-1 {F(s)} = L^-1 {1/ (s^2 + 16)}

f(t) = sin(4t)/4