High-Order Ordinary Differential Equations with More Derivatives (from Physics)

Here we show how to derive higher-order differential equation systems, with higher-order derivatives, from F=ma by chaining together simple systems. Our example is combining two spring-mass systems to get a fourth order equation.
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This video was produced at the University of Washington
%%% CHAPTERS %%%
0:22 General Higher-Order Differential Equations
3:55 Where Do High-Order ODEs Come From?
11:47 Procedure to Derive Higher-Order ODEs from F=ma
14:33 Example Derivation for Spring-Mass System

[@keyreeves4631]

How is this guy producing so much content about a variety of highly complicated topics in such a short timespan…. What the hell

[@CodyKoehler]

He is a top tier professor with experience and passion.

[@olivioarmandocordeirojunio8280]

I love your classes. You make the world a better place to live. Thank you very much.

[@olivioarmandocordeirojunio8280]

Hi. I think there is a mistake at 15:56. You used d(X_1)/dt but it is just X_1.

[@ruddytapia2676]

True

[@diveintoengineering6089]

Yes. No damping son no xdot I think. Excellent video anyway. Thank you!

[@whootoo1117]

I really love your explanations and the way you explain complex things into the basic blocks. I liked the way you changed the 2 functions into their fourth order!

[@rudypieplenbosch6752]

Thanks for these lectures, 2nd order now indeed I got more comfortable with, time for more complicated systems.

[@zjinup]

Can’t wait to see the next video! Thank you!

[@Edruezzi]

It's amazing how many of the vital equations of physics and hence engineering have derivatives of second order.

[@TheEicio]

In the second portion of step A, an x-dot term was added that I don’t understand. This leads to x-triple dot, etc.

[@ClydeMcQueen]

There's an error at 15:55, it should be just x, not x-dot.

[@edisonj5335]

there’s a mistake sir！no x triple dot here

[@eig_himanshu]

Sir...could you upload videos on potential theory relating to complex analysis

[@Eigensteve]

I have that in another playlist on vector calculus and PDEs

[@curtpiazza1688]

Great! 😊

[@lioneloddo]

Wow, it's too much complicated!
Human brain is not programmed to do things like that!
Emmanual Kant wrote that mathematics was created by Thales by chance. Exepted few people in the world, nobody can do this kind of things!

[@coraltown1]

I'm still not clear on how to convert those two 2nd order ODEs to four 1st order ODEs.