Find the inverse Laplace transform of 6s8 s2 15 s0SolutionSo

Find the inverse Laplace transform of (6s+8)/( s^2 +15) s>0

Solution

Solution: (6s+8) / (s^2+15)   can be written as

      = (6s / (s^2+15) ) + (8 / (s^2+15) )

      = 6 (s / (s²+(sqrt15)²) + (8/sqrt15) (sqrt15 / (s² + (sqrt15)²))

The inverse laplace transform of the above equation is    

= 6 cos (sqrt15)t + (8/sqrt15) sin (sqrt15)t