Calculate the inverse Laplace transforms of the following functions without applying partial-fraction expansion and verify the results by MATLAB®: (a) X(s) = 6s/(s2 + 9)2 . (b) X(s) = 1/(s3 + 4s2 )....

Calculate the inverse Laplace transforms of the following functions without applying partial-fraction expansion and verify the results by MATLAB®:

(a) X(s) = 6s/(s2 + 9)2 .

(b) X(s) = 1/(s3 + 4s2 ).

Use the convolution theorem to determine the inverse Laplace transforms of the following functions:

(a) X(s) = 1/(s2 - ~2 ) 2 .

(b) X(s) = 1/[s2 (s2 + a)].