Question

Previous ProblemP Problem List Next Problem 48 +8 s2 +1 (1 point) Find the inverse Laplace transform f(t) = L 1 8)) of the function F(s) = help (formulas) s2 +1 Preview My Answers Submit Answers

Answer 1

l inverse {-4s+ 8/s^2 + 1} = f(t) therefore f(t) = -4 L inverse {s/s^2 + 1}-8 L inverse {1/s^2 + 1} L inverse{1/s^2 + 1} = sint we know , if L inverse {f(s)} = f(t) and f(0) = 0 then L inverse {sf(s)} = f'(t) sin 0 = 0 therefore L inverse { s/s^2 + 1} = d/dt sint = cost therefore f(t) = l inverse { -4s+ 8/s^2 + 1} = -4 cost -8 sint therefore f(t) = -4 cos(t) - 8 sint f(s) = 18s/s^2-81 f(t) = l inverse {18s/s^2-81} = L inverse { g/s + g +g/s-g} = g L inverse { 1/ s + g } + g L inverse {1/s-g} = g e^-gt + g e^gt therefore f(t) = ge^-gt +ge^gt.

Answer 2

1. -(4cost+8sint) 2. 9e^-9t+9e^9t