Physics Help Forum Laplace Transformation
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 Mar 9th 2009, 09:47 AM #1 Junior Member   Join Date: Feb 2009 Location: Dhaka,Bangladesh Posts: 6 Laplace Transformation Hello, I am facing problem understanding the following equation I have just faced. It will be very kind of you if you can clarify it to me. The equation is...... L [f(at)] = 1/a*F(s/a) I can not find the "F(s/a)" where does it come from? And what does it mean? I have started Laplace Transform lately and to understand it completely. If you can help me I would be very glad. Thank you.
 Mar 9th 2009, 06:07 PM #2 Senior Member   Join Date: Dec 2008 Location: Las Cruces NM Posts: 256 When you take the Laplace transform of a function $\displaystyle f(t)$ of the varible $\displaystyle t$, you get a function $\displaystyle F(s)$ of a different variable $\displaystyle s$. The rule $\displaystyle {\cal L} f(at) = \frac {1}{|a|} F(s/a)$ tells you how to find the Laplace transform of $\displaystyle f(at)$ when you only know the Laplace transform of $\displaystyle f(t)$. For example, given that $\displaystyle {\cal L} \sin(t) = \frac {1}{s^2 + 1}$, find $\displaystyle {\cal L} \sin(3t)$. $\displaystyle {\cal L} \sin(3t) = \frac {1}{|3|} \frac {1}{ (s/3)^2 + 1}$ $\displaystyle = \frac {1} {3} \frac {1}{ \frac {s^2}{ 9} + 1}$ $\displaystyle = \frac {3}{9} \frac {1}{ \frac {s^2}{ 9} + 1}$ $\displaystyle = \frac {3}{s^2 + 9} = \frac {3}{s^2 + 3^2}$
 Mar 9th 2009, 08:56 PM #3 Junior Member   Join Date: Feb 2009 Location: Dhaka,Bangladesh Posts: 6 Thanks a lot sir, I was thinking that "F" could be another kind of function. Thank you for your easy solution. I will be glad if you please send me the derivation. I will try it myself but it will be good for me if you send it. Thank you.

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