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Re: laplace transform

• To: mathgroup at smc.vnet.net
• Subject: [mg65105] Re: laplace transform
• From: "Scout" <Scout at nodomain.com>
• Date: Wed, 15 Mar 2006 06:28:16 -0500 (EST)
• References: <dv68hj$nvj$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

<Marlies.Goorden at physics.unige.ch>
news:dv68hj$nvj$1 at smc.vnet.net...
> 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
>
Hi,
you might to use Assumptions with LaplaceTransform:

    In[1]:= 
LaplaceTransform[Sin[a*t],t,s,Assumptions\[Rule]a\[Element]Reals]

to obtain:  a/(s^2+a^2).

Bye,
    ~Scout~