So you know that we are now already in this part of the course where we will apply the concepts that
we have learned so far to difficult physical problems.
So you know that in the previous section, we have used derivatives and integrals to solve differential
equations.
And now we will apply other concepts like the future transforms also the fitting procedures that we
have described previously.
So here we will solve a single example, which is actually very difficult.
We will have a couple of multiple harmonic oscillators, for example, several pendulums, and we will
investigate how these pendulums interact with each other and why the motion changes.
So it turns out we can formulate the differential equations that describe this problem in terms of a
matrix.
And when we calculate the so-called eigenvalue of this matrix, then this will tell us about the characteristic
frequencies of the individual oscillators.
So here we will learn about this concept of matrices and calculating their eigenvalues.
But then we will also apply the concept of the free to transform and the fitting procedures which we
have learned previously.
And we will see that here.
Also, these characteristic frequencies play a very important role.
So it seems like all of these three parts come together here and give us a better understanding of this
coupled motion of these harmonic oscillators.
So as I said, it's a very difficult problem, but these three methods help us enormously in understanding
what is actually going on here.
So I hope you are excited and let's get started.
Let's start with the programming.