00:01
All right, so here we want to take the inverse laplace transform of 1 over s squared plus 9 s plus 20.
00:09
And so our hope is that we can factor.
00:12
So let's see if we can do that.
00:15
It looks like it does factor s plus 4 times s plus 5 does work.
00:21
Excellent.
00:23
Next, we need to find we're going to split it up as partial fractions.
00:27
So we need to split up and find our constants.
00:30
For now, we'll call it a over s plus 4 and b over s plus 5.
00:36
So if we were to re -combine the fraction to the original, i would do a common denominator, so i would go a times s plus 5 plus b times s plus 4.
00:49
And that has to equal my original 1.
00:52
So let's distribute out.
00:54
So we get a -s plus 5a plus b -s plus 4b.
01:00
Equals 1.
01:02
Now notice there's no terms with an s on the right, therefore a plus b has to equal 0, but 5a plus 4b has to equal 1...