00:01
All right, now let's have fun solving laplace transform.
00:05
So let's first take a look at the one in the left in blue.
00:10
Basically, we have our basic function is cosine of 3t.
00:14
We have an exponential multiplier, which provides a shift in the frequency domain.
00:20
And seven just goes along for the right.
00:22
So let's start going.
00:23
Okay, so f of s.
00:24
I first write what would normally be cosine.
00:27
And cosine is normally by itself would be s.
00:32
Over s squared plus nine.
00:35
But we have a shift in every s.
00:37
So instead we're going to write, let me clear it off.
00:42
We have to deal with the shift.
00:46
So instead i'm going to write s minus 2 over s minus 2 squared plus 9.
00:54
I still have the 7 as a multiplier.
00:56
And those are easy.
00:57
They just go along for the ride.
00:59
So seven times that.
01:00
So that's the first term.
01:02
Okay, second term has sign.
01:05
Sign is our basic function.
01:07
Our basic function would normally have something like s squared plus 25 over five.
01:15
But again, we have a shift, but the shift is only in this s.
01:18
So let's redo it.
01:20
Okay, so we are going to have a shift of seven.
01:26
So i'm going to have a five.
01:28
I'm going to have a shift of seven.
01:29
I'm going to have a shift of seven in the time domain.
01:32
And i still has, i took care of that and i still have a two multiplier.
01:37
So i could go ahead and clean this one up a little bit.
01:40
Whoops, that should be a best.
01:42
Okay, so then i get, i'll just leave that one as is, seven times s minus two over s minus two squared plus nine minus ten over s minus seven squared plus 25.
02:01
Okay, so that's a final little plus transform the function on the left.
02:06
Let's go ahead and do the one on the right now.
02:09
Okay, this one only has one term.
02:12
It's a cosine again.
02:13
I believe this is actually supposed to be a 3t, so let's fix that...