Question

Find f(t) for each of the following function
F(s) = 320/s ²(s+8)

Answer 1

To find f(t) for F(s) = 320/s²(s+8), we need to find the inverse Laplace transform. The answer is f(t) = 320t - 320e^(-8t).

Step-by-step explanation:

To find f(t) for F(s) = 320/s²(s+8), we need to find the inverse Laplace transform of F(s). Using partial fractions, we can break down F(s) into two terms: 320/s² and -320/((s+8)). The inverse Laplace transform of 320/s² is 320t, and the inverse Laplace transform of -320/((s+8)) is -320e^(-8t).

Therefore, the function f(t) can be written as f(t) = 320t - 320e^(-8t).