inverse laplace Determine the inverse Laplace transform of the following functions using partial fractions where necessary: Solution 1. s/(s^2 - 16) = s/(s^2 - 4^2) = s/{(s + 4)(s - 4)} = 1/2[s/(s + 4) + s/(s - 4)] then inverse laplace transform 1/2[s/(s + 4) + s/(s - 4)] = 1/2[(e^(-4t) + e^(4t)] 2. s/(s^2 + 2) = s/(s^2 + sqrt(2)) then inverse laplace transform s/(s^2 + sqrt(2)) = cos(sqrt(2)t) 3. inverse laplace transform (5s + 4)/s^3 = 2t^2 + 5t inverse laplace transform - {(2s-18)/(s^2 + 9)} = -2 (cos(3 t)-3 sin(3 t)) and inverse laplace transform 24/s^4 = 4t^3.

1. inverse laplace Determine the inverse Laplace transform of the following functions using partial
fractions where necessary:
Solution
1. s/(s^2 - 16) = s/(s^2 - 4^2) = s/{(s + 4)(s - 4)} = 1/2[s/(s + 4) + s/(s - 4)]
then inverse laplace transform 1/2[s/(s + 4) + s/(s - 4)] = 1/2[(e^(-4t) + e^(4t)]
2. s/(s^2 + 2) = s/(s^2 + sqrt(2))
then inverse laplace transform s/(s^2 + sqrt(2)) = cos(sqrt(2)t)
3. inverse laplace transform (5s + 4)/s^3 = 2t^2 + 5t
inverse laplace transform - {(2s-18)/(s^2 + 9)} = -2 (cos(3 t)-3 sin(3 t))
and inverse laplace transform 24/s^4 = 4t^3