inverse laplace transform, example#4, with partial fraction

inverse laplace transform,
inverse laplace transform example,

blakcpenredpen

[not_potaytoes_hobbit]

I had never seen this method for solving partial fractions in the 4 years I have spent in college and it's a life saver, thank you!

[christianelzey]

BEST explanation I have seen so far. Thank you very much.

[DrQuatsch]

Yeah, I did it in a completely different way! I completed the square at the bottom: s^2 + 2s - 3 = (s + 1)^2 - 2^2. Then I split the inverse laplace transform into: L^-1{(s + 1)/((s+1)^2 - 2^2)} + L^-1{3/((s+1)^2 - 2^2)}. The s+1 gives us a common factor of e^-t, so it becomes e^-5 * (L^-1{s/(s^2 - 2^2)} + 3/2 L^-1{2/(s^2 - 2^2}) = e^-t * (cosh(2t) + 3/2 sinh(2t)).
If you substitute the cosh and sinh for their e-power forms, it results in the same answer, obviously.

[joel]

this is going to save my butt on my signals and systems test tommorow. thank you

[Rstshclfrd]

Thanks dude Youre really good at explaining in a good pace Really helped me comprehend

[maxw]

Thank you I couldn't find any comprehensive explanation of the inverse laplace apart from these videos

[jkuebler]

Oh my gosh this is why you are my favorite. Took something scary and made digestible.

[brayschway]

This was more than helpful. Thanks a ton!

[JacobPorterLadder]

where were these videos 5 years ago when i was in school. studying for my FE and these are a Lifesaver (make sure you take your FE before you graduate kids)

[BillFye]

Is it wrong to use completing the square with this problem? Do you have to use partial fraction?

[emilyroberts]

I used completing the square on the denominator and got a different answer: e^(-t)*[cos(2t)+3sin(2t)] - did I do something wrong?

[mccoy]

What concept did you apply on getting the numerator of the right side?

[golmolenahisidhibaatein]

Hi,
perfect.
Is laplace inverse of (2/p^2-2p)= 2e^2t.
or we apply Convolution theorem of inverse laplace.
or
2 L'(1/(p-1)^2-1)=2/1 (Sinht).
sir pls reply.

[luc]

thx saved me an hour to study this topic

[pinkynicolettecabalog]

thank you for this! based from inverse laplace table

[Danish]

What if you have 3 terms as the denominator? Do you do faction over fraction over fraction?

[hizmoryyii]

what if the denominator for both is equal?

[soomaseirt]

Thanks for helping, and deliver the issue of the issue if it executed F (s) = s-1 / s3 + 2s2 + s

[abhishekchakrabarty]

I did it with another concept and my answer comes epow(-t)[cos2t+1.5sin2t] Is it right?

[helloitsme]

Can you do this with completing the square on the bottom and using the translation theorem please