# Math Help - La place inverse

1. ## La place inverse

F(s) = s+1/(s^2 + 2s + 10)^2 Find the La place inverse transform

2. Originally Posted by mahm32
F(s) = s+1/(s^2 + 2s + 10)^2 Find the La place inverse transform
You have $F(s) = \frac{s + 1}{([s + 1]^2 + 3^2)^2} = G(s + 1)$ where $G(s) = \frac{s}{(s^2 + 3^2)^2}$.

From a well known theorem: $LT^{-1}[G(s + 1) = e^t g(t)$ where $g(t) = LT^{-1}[G(s)]$.

To get g(t), first note that $G(s) = \frac{dK}{ds}$ where $K(s) = - \frac{1}{2} \left(\frac{1}{s^2 + 3^2} \right)$.

Now use the well known theorem that $LT^{-1}\left[\frac{dK}{ds}\right] = - t k(t)$ where $k(t) = LT^{-1}[K(s)]$.

3. Thanks a lot .