The inverse Laplace transform

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ENG99

Joined Feb 13, 2014
37
I have tried to solve this problem and I did the first part of it, but I don't know how could I get the final answer in terms of h(t)=..................

Please see the pic attached.
 

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WBahn

Joined Mar 31, 2012
26,398
And keep in mind that you often need to play with the form of what you have in order to get it into one of the forms in the tables you are using.
 

WBahn

Joined Mar 31, 2012
26,398
That is usually a good deal easier than evaluating the integral.
Almost always easier. It's good to evaluate a few forward and inverse integrals just to see what's involved and that the tables are magical -- but in practice you play as many games as you can to avoid evaluating the integral first, if for no other reason than if what you are working with isn't already in the table, then the integral is going to be a stone bitch.
 

WBahn

Joined Mar 31, 2012
26,398
I must confess, that the last time I did one of those integrals I was an undergraduate.
That's the point at which most people do them -- usually in Diffy-Q about midway through their undergraduate program. If you go further and take a complex variables course you often do them from a different perspective using contour integration (IIRC) and that may or may not be at a graduate level. When a friend and I were studying for the PhD qualifiers we went and derived a good portion of a basic table just for the general practice it offered.
 

MrAl

Joined Jun 17, 2014
8,231
And keep in mind that you often need to play with the form of what you have in order to get it into one of the forms in the tables you are using.
Hi,

I have to agree 100 percent, because at first it seems like there should be an exact entry in the table, but sometimes it requires a little algebraic juxtaposition to get the right form. Very good advice.

As a side note, there are other techniques other than pure integration, but i have a feeling we should leave that for some other time.

Also, the last time i evaluated the integral directly was back sometime in the 1990's, and it took a whole page of hand written stuff to get the result for a simple RC circuit excited by a unit step. It was fun i guess, and with a trip to the library i also learned another way to do it using a special class of integrals (not the direct ILT integral). That was interesting too but it's been so long i'd have to look it up again as i never used either of these methods again (ha ha).
I dont know if i should mention that there are online resources too, that will evaluate and pop out the answer, but i hate to see anyone do that way before they have done it the old fashioned way with tables and a little thought behind it first.
 
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