Help in Laplace and Inverse Laplace evaluation...

[Cluene]

Hi, we have been given a series of Laplace problems as our homework which is unfortunately due tomorrow and unfortunately I still have some numbers lefts unsolved. I was wondering if you could give me an idea how to evaluate the unsolved numbers and if your so kind to verify my answers to some numbers? ... please (T_T) desperately need help....here is an attachment of the problems [the numbers needed to be solved are 1-8 and 15-40, don't mind the 45-48 I'll deal with that later .. I hope]and here is the attachment for the numbers that I have solved and tried to solved.I'm sorry for the bad penmanship, I'm in kind of a hurry.Your help is greatly appreciated...

 

[galactus]

I do not know about anyone else, but I can not read that.

Type up a problem you would like help with.

But, I doubt if anyone is going to go through 30+ homework problems.

If you need help with LaPlace, post a particular problem.

 

[Cluene]

oops hahah my bad, i thought it was downloadable XD okay2 hmmmmmm how about these one.... how do i find the inverse laplace of these ones:

30.) e^(-2s) / (s^2+4)

41.) 1/s tan^-1 (1/s)

 

[galactus]

Here's help with the first one.

This is a unit step.

Since \(\displaystyle F(s)=\mathcal{L}\left\{f(t)\right\}, \;\ a>0\), then \(\displaystyle \mathcal{L}\left\{f(t-a)\mathcal{U}(t-a)\right\}=e^{-as}F(s)\)

Now, knowing that \(\displaystyle \mathcal{L}^{-1}\left\{\frac{1}{s^{2}+4}\right\}=\frac{1}{2}sin(2t)\), we get:

\(\displaystyle \frac{1}{2}sin(2(t-2))\mathcal{U}(t-2)\)