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So you know that we are now already in this part of the course where we will apply the concepts that

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we have learned so far to difficult physical problems.

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So you know that in the previous section, we have used derivatives and integrals to solve differential

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equations.

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And now we will apply other concepts like the future transforms also the fitting procedures that we

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have described previously.

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So here we will solve a single example, which is actually very difficult.

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We will have a couple of multiple harmonic oscillators, for example, several pendulums, and we will

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investigate how these pendulums interact with each other and why the motion changes.

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So it turns out we can formulate the differential equations that describe this problem in terms of a

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matrix.

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And when we calculate the so-called eigenvalue of this matrix, then this will tell us about the characteristic

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frequencies of the individual oscillators.

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So here we will learn about this concept of matrices and calculating their eigenvalues.

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But then we will also apply the concept of the free to transform and the fitting procedures which we

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have learned previously.

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And we will see that here.

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Also, these characteristic frequencies play a very important role.

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So it seems like all of these three parts come together here and give us a better understanding of this

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coupled motion of these harmonic oscillators.

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So as I said, it's a very difficult problem, but these three methods help us enormously in understanding

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what is actually going on here.

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So I hope you are excited and let's get started.

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Let's start with the programming.