Laplace transform of a piecewise function

[Lorens]

What is the laplace transform of

http://img150.imageshack.us/img150/8145/laplacetransform6wk.jpg

 

[quantumdude]

According to the section entitled "Homework Help" in the Physics Forums Global Guidelines which you agreed to:

NOTE: You MUST show that you have attempted to answer your question in order to receive help.

So what are you got?

 

[Lorens]

According to the section entitled "Homework Help" in the Physics Forums Global Guidelines which you agreed to:
So what are you got?

It isn't so much to test, just to watch a tabel of formula, i know the transform for cos(x), but i can't find any rule which would let me multiplicat it with O(x).

I mean for problems like this you just think, and try to figure out how to do it.
I would say my problem is O(x).

Anyway i got to go to bed now 00:08.. lol...

 

[quantumdude]

Do you know what $\theta(t)$ is?

 

[Lorens]

Do you know what $\theta(t)$ is?

for $\theta(t)$ t<0 gives t=0 and t>0 gives t=1 and the transform is 1/s, but that knowledge don't help me much :( ...

 

[quantumdude]

You are right about $\theta(t)$, but that knowledge should help you a great deal.

You have a function that is defined piecewise:

$$\theta(t) = \left\{ \begin{array}{cc}0 & t<0\\1 & t \geq 0\end{array}$$

Now, if you multiply $\theta(t)$ by $\cos(t)$, then you just have to multiply both pieces by $\cos(t)$.

So...

$$\cos(t)\theta(t) = \left\{ \begin{array}{cc}0 & t<0\\\cos(t) & t \geq 0\end{array}$$

Can you take it from there?

 

[Lorens]

You missed that $\theta(o)$=1/2 my textbook say so, but it don't matter.

Can I ignore $\theta(t)$ seen the laplace transform isn't defined for the second quadrant for the x-axis.

Also i must ask how do you get access to all the special signs?

Thx for your time Lorenz

 

[Galileo]

Can I ignore $\theta(t)$ seen the laplace transform isn't defined for the second quadrant for the x-axis.

It's not a matter of being undefined, but you got the right idea. It's more precise to state that the laplace transform of f doesn't care what values f takes on for x<0.

Also i must ask how do you get access to all the special signs?
Thx for your time Lorenz

What special signs?

 

[Lorens]

Like $\theta(t)$ i just copyed him there

 

[Galileo]

Ah, you mean LateX.
https://www.physicsforums.com/showthread.php?t=8997
The best way to get acquainted with it is to see other people's codes
Just steal..ehm..look at the code by clicking on the expression.