Question

Determine the inverse Laplace transform of the function below. 2 2 St + 49 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms s2+ 49

Answer 1

Inverse Laplace transform of 2/s^2 + 9 let F(s) = 2/s^2 + 49) = 2 L^-1 (1/s^2 + 49) = 2 L^-1 (1/s^2 + 7^2) we know that L^-1 (1/s^2 + a^2) = 1/a sin a t therefore L^-1 (1/s^2 + 7^2) = 1/7 sin 7 t therefore L^-1 (2/s^2 + 49) = 2 middot (1/7 sin 7 t) = 2/7 sin 7 t therefore L^-1 (2/s^2 + 49) = 2/7 sin 7 t