# Finding Laplace Transform using first shifting theorem

• September 6th 2008, 01:52 AM
ghazala
Finding Laplace Transform using first shifting theorem
1. Find the Laplace transform of e^(-2t) sinηπt
• September 6th 2008, 02:24 AM
mr fantastic
Quote:

Originally Posted by ghazala
1. Find the Laplace transform of e^(-2t) sinηπt

Where are you stuck?

Theorem: $LT\left[ e^{at} f(t) \right] = F(s - a)$ where $F(s) = LT[f(t)]$

In your case a = -2 and $f(t) = \sin (nt)$. You should be able to look up a table of Laplace transforms to get F(s) .....
• September 6th 2008, 03:05 AM
ghazala
yup thts wht i did..

i got this answer:

(ηπ + 2)/ (ηπ + 2)^2 + s^2

i think i made a mistake smwhere :S
• September 6th 2008, 04:58 AM
mr fantastic
Quote:

Originally Posted by ghazala
yup thts wht i did..

i got this answer:

(ηπ + 2)/ (ηπ + 2)^2 + s^2

i think i made a mistake smwhere :S

Laplace transform of $f(t) = \sin (nt)$ is $F(s) = \frac{n}{s^2 + n^2} \, ....$
• September 6th 2008, 06:28 AM
ghazala
thank you :)