- #1
Pouyan
- 103
- 8
Homework Statement
find the inverse Laplace transform of the given function by
using the convolution theorem
Homework Equations
F(s) = s/((s+1)(s2)+4)
The theorem : Lap{(f*g)(t)} = F(s)*G(s)
The Attempt at a Solution
I know how to find it the answer is :
we have 1/(s+1) * s/(s+4) and the inverse of each of these functions are : e-t * cos(2t)
further the answer is : ∫(e(-(t-τ))*cos(τ)dτ)
But if I try to solve this problem without convolution theorem; and with partial fraction I get :
s/((s+1)(s2+4)) = (1/5) ( (1/(s+1) + s/(s2+4) + 4/(s2+4) )
and the inverse of this function is :
(1/5) (cos(2t) - e-t +2sin(2t))
MY QUESTION IS :
∫(e(-(t-τ))*cos(τ)dτ) = (1/5) (cos(2t) - e-t +2sin(2t)) is this right ?