00:01
So we have this pair of ode's.
00:02
What we want to do is find the item values and eigen vectors and other things.
00:10
And so what i want to do is write this as a matrix equation.
00:53
Right.
00:53
So if, call capital u or just u is, so i'll call capital u that column vector.
01:09
So we got, and then i'm going to make an assumption that u is some e0, which is the column vector times.
01:30
We have this pair of ordinary differential equations that we want to solve.
01:38
So the first thing i'm going to do is write it as a matrix equation like that.
01:54
Then i'm going to define capital u as that column vector.
02:03
And we expect it to look in like this, where it's going to have some constant.
02:09
Column vector times a cosine omega -t.
02:12
We're interested in finding the frequencies, the so -called eigenfrequency.
02:19
So if i plug that in, if i take the second derivative, i get a minus sign with an omega -squared multiplying that, and then we got this.
02:37
So we get this equation for u -0...