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 General Physics General Physics Help Forum 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.  Tags laplace, transformation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post webconnector Advanced Electricity and Magnetism 6 Jul 9th 2015 01:18 PM mooshazz Electricity and Magnetism 1 May 18th 2013 07:31 AM Nimmy Advanced Electricity and Magnetism 0 Oct 18th 2011 09:42 AM aaaa202 Special and General Relativity 0 Oct 10th 2011 06:28 AM rosalia General Physics 0 Apr 22nd 2009 09:49 AM