00:01
So we're supposed to solve this equation using laplace transforms.
00:05
So one of the problems with laplace transforms is it's hard to apply, or not hard, but it's not straightforward to apply boundary conditions that aren't at zero.
00:19
Zero.
00:19
Okay.
00:20
So what i'm going to do is i'm going to define two more, what are essentially initial conditions.
00:44
These are the values of what our derivatives are at the origin.
00:54
Okay.
00:55
And then what i'll do, i'll go through the laplace transform thing.
01:00
I'll get to my final function for y of t and then i'll apply the boundary conditions and figure out what a and b are.
01:13
All right so i am going to divide through by e i so i get an equation that looks like this.
01:39
Okay and i'm actually going to define this quantity.
01:46
I'm going to call it alpha.
01:48
It's just a kind of a strength kind of thing.
01:53
What it actually means is an important, it's just a constant.
01:58
And so i don't have to keep writing this out.
02:00
All right.
02:01
So i'm going to define y of s, this laplace transform of y of x...