Laplacian Inverse Calculation

**ragnar** · April 3rd 2011, 08:32 AM

So I'm to find $\mathcal{L}^{-1}\{e^{-\pi}}/(s^{2}+1)\}$ and I figure it should just be: The exponential tells me its unit step-functioned over by $\pi$ and then just Laplacian inverse the leftover so the result is $\sin(t-\pi) \mathcal{U}(t-\pi)$ . My book says it's $-\sin t \mathcal{U}(t-\pi)$ and I don't get it.

**topsquark** · April 3rd 2011, 08:36 AM

Originally Posted by ragnar

So I'm to find $\mathcal{L}^{-1}\{e^{-\pi}}/(s^{2}+1)\}$ and I figure it should just be: The exponential tells me its unit step-functioned over by $\pi$ and then just Laplacian inverse the leftover so the result is $\sin(t-\pi) \mathcal{U}(t-\pi)$ . My book says it's $-\sin t \mathcal{U}(t-\pi)$ and I don't get it.

Isn't sin(t - Pi) = -sin(t)?

-Dan

**ragnar** · April 3rd 2011, 08:38 AM

Yep, just didn't see it because I'm retarded. Thanks.

**topsquark** · April 3rd 2011, 08:41 AM

Originally Posted by ragnar

Yep, just didn't see it because I'm retarded. Thanks.

Don't beat yourself up. We've all been there.

-Dan

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