Re: laplace transform
- To: mathgroup at smc.vnet.net
- Subject: [mg65100] Re: [mg65076] laplace transform
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Wed, 15 Mar 2006 06:28:13 -0500 (EST)
- References: <200603141059.FAA24086@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Marlies.Goorden at physics.unige.ch wrote:
>Hi,
>I have a problem with the Laplace transform of mathematica. I
>want to know the laplace transform of sin(a*t).
>When I type
>LaplaceTransform[sin(a*t),t,s]
>mathematica gives me
>\sqrt(a^2) sign(a)/(a^2+s^2)
>
>On the other hand my mathematics books gives the answer
>a/(s^2+a^2)
>
>For complex a the answer is not the same. If I choose for
>example
>a=0.3+0.5i and
>s=1
>the two formulas give me
>-0.096+0.65i and 0.51+0.41i respectively.
>
>A numerical integration,
>i.e. NIntegrate[Sin((0.3+0.5i)*t)*Exp[-t],{t,0,Infinity}]
>gives me the same numerical value as the mathematics book
>formula.
>Is the mathematica formula wrong?
>Thank you for your help,
>Marlies Goorden
>
>
>
Possibly the reason for the Sign[a] might be that the Laplace transform
has a switch at the origin depending on the sign of a
In[1]:=
Plot[With[{a=1},LaplaceTransform[Sin[a*t],t,s]],{s,-10,10}]
Plot[With[{a=-1},LaplaceTransform[Sin[a*t],t,s]],{s,-10,10}]
Assuming[a>0,LaplaceTransform[Sin[a*t],t,s]]//InputForm
Assuming[a<0,LaplaceTransform[Sin[a*t],t,s]]//InputForm
Out[1]=
â??Graphicsâ??
Out[2]=
â??Graphicsâ??
Out[4]//InputForm=
a/(a^2 + s^2)
As to the complex vals, I don't see a problem
In[5]:=
With[{a=0.3+0.5*I,s=1},LaplaceTransform[Sin[a*t],t,s]]//N
Integrate[Sin[(0.3+0.5*I)*t]*Exp[-t],{t,0,â??}]
Out[5]=
0.505279\[InvisibleSpace]+0.414781 \[ImaginaryI]
Out[6]=
0.505279\[InvisibleSpace]+0.414781 \[ImaginaryI]
Hope this helps
Pratik
- References:
- laplace transform
- From: Marlies.Goorden@physics.unige.ch
- laplace transform