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December 30th, 2012, 12:07 PM   #1
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Laplace transform

Hi there,

I just started to learn the laplace transform.
I know that the transform for
gamma(t)= 1/s

But how do you perform a transformation on gamma(sin(?t)) ?
Thanks in advance!

Greetings,
Frederic
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December 30th, 2012, 12:26 PM   #2
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Re: Laplace transform

??

I know that



or I think you mean that

if you mean by gamma the laplace transformation ?
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December 30th, 2012, 12:32 PM   #3
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Re: Laplace transform

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December 31st, 2012, 06:05 AM   #4
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Re: Laplace transform

Im sorry,
what I meant was the laplace transform of the unit step of sin(?t).

So L( u(sin(?t))) = ?
How can i deal with this problem?
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December 31st, 2012, 06:10 AM   #5
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Re: Laplace transform

Let me post it like this:

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December 31st, 2012, 11:46 AM   #6
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Re: Laplace transform

Quote:
Originally Posted by fredericP
Im sorry,
what I meant was the laplace transform of the unit step of sin(?t).

So L( u(sin(?t))) = ?
How can i deal with this problem?
Sorry never heard of unit step of sin (t) !
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January 1st, 2013, 08:30 PM   #7
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Re: Laplace transform

Quote:
Originally Posted by fredericP
Im sorry,
what I meant was the laplace transform of the unit step of sin(?t).

So L( u(sin(?t))) = ?
How can i deal with this problem?
I may be way off base here, but if the unit step is defined as



then is a periodic square wave with a period of 2. For example, it has a value of 1 from t = 0 to 1, 0 from t = 1 to 2, 1 from t = 2 to 3 and so on (I am being a bit sloppy here with overlap at the endpoints, but hopefully the waveform values are clear).

I will not try to take the LT of but I will take the LT of (at least according to how I defined it). Multiplying by U(t) makes the waveform equal to 0 for t<0. Otherwise, strange things tend to happen (convergence problems, I guess).

I had to dust off a (very) old textbook for this, but let's define a function, f, for the first period:

whose LT is

Now we add in the periodic nature of the waveform by noting that:

and the LT of is:



Since



So

Do you know if this is anywhere close to the answer?
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