More Examples of Second Order Differential Equations

This video gives more examples of second-order Ordinary Differential Equations and their solutions. We review the characteristic polynomial and how to use initial conditions. We also show that eigenvalues of the matrix system are roots of the characteristic polynomial.


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This video was produced at the University of Washington

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0:21 First Example
11:23 Writing as a Matrix System of Equations
16:11 Matlab Code Example: Plotting and Integrating the Solution
23:14 Matlab Code Example: Plotting and Integrating the Solution
25:23 Second Example (Unstable System)
28:33 Third Example

[ahmedbassam]

The quality and the preparation is just amazing. Thanks a lot for giving this for free on YouTube

[gjircdn]

Thankyou Steven, you are a very good teacher.

[danhvo]

I hope the "like button" will be effective for multiple clicks. Great lecture.

[lioneloddo]

I don't remenber very well, but I believe that we can use two other constants which have a more physical meaning.
Instead of using two exponentials, we can use : A.cos(wt+phi) where the two equivalent unknown are A and phi (the amplitude and the phase).
We can also use A.cos(wt) + Bsin(wt) where the 2 unknown are A and B (just two ampltitudes without phase).
It's less beautiful (from a mathematical point of view) but sometimes it's more practical ...

[danilomoura]

great lecture!! I am learning a lot! thx!

[starriet]

for future ref) I haven't investigated how the ODE45(or 'solve_ivp' in Python code) works, but the parameter 't' of the lambda function @(t, y)A*y seems like "dummy", just for making the ODE45 work.

[steadyfield]

Great video. But what if the right hand side of the differential equation in 9:00 is a non-zero constant (i.e. the system is non-autonomous and has an external control input), how to solve the equation by assuming x(t) = exp(λ*t)?

[davidmurphy]

I paused the video at 1:39 and did the sum no problem. I've also done a lot of linear algebra, built a 3d graphics engine from scratch, make a neural net, games, etc. Wouldn't call myself an expert by a long shot but this is all stuff I'm reasonably familiar with.

20 mins into the video I was completely lost. On maths that I can do. Wow.

Maybe this isn't the right channel for me...