# Thread: Laplase Transformations! PLEASE HELP!!

1. ## Laplase Transformations! PLEASE HELP!!

Find the Laplace transformation:
I think a convolution is necessary, Please Help!

2. Originally Posted by Bananna
Find the Laplace transformation:
I think a convolution is necessary, Please Help!
Nice question

By sifting property,

$\displaystyle \cos(t) \delta(t-3\pi) = \cos(3\pi) \delta(t-3\pi)$

Now do you know the Laplace Transform of a shifted impulse?

3. and

But I dont know how they go together
Please help

4. NO!
$\displaystyle \cos(3\pi) = -1$, it is a constant...
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Originally Posted by Bananna
and

But I dont know how they go together
Please help
If c is a constant and $\displaystyle L(\delta(t-3\pi)) = e^{-3\pi s}$

Then what is $\displaystyle L(c\delta(t-3\pi)) \text{ ?}$

5. duh....I have been staring at these problems.
L(1)=1/s
so the L(-1) must be -1/s

6. Originally Posted by Bananna
duh....I have been staring at these problems.
L(1)=1/s
so the L(-1) must be -1/s
Right.. so what is

7. Originally Posted by Isomorphism

NO!
$\displaystyle \cos(3\pi) = -1$, it is a constant...
--------------------------------------------------------------------

If c is a constant and $\displaystyle L(\delta(t-3\pi)) = e^{-3\pi s}$

Then what is $\displaystyle L(c\delta(t-3\pi)) \text{ ?}$

is that it?

8. Originally Posted by Isomorphism
Right.. so what is

...???

9. Originally Posted by Bananna
Find the Laplace transformation:
I think a convolution is necessary, Please Help!
Are you trying to get the Laplace transform of the product? If so, just use the definition:

$\displaystyle LT[\cos (t) \delta(t - 3 \pi)] = \int_{0}^{\infty} e^{-st} \, \cos (t) \delta(t - 3 \pi) \, dt$

and use the sifting property of the Dirac delta function.