Lagrangian Mechanics: Table with a hole, two masses connected by string

This is part of my classical mechanics series. You can find all my videos in the series in the following playlist.
• Classical Mechanics 1 F24
A mass is hanging vertically from a string that passes through a hole in a frictionless table. On the table, the string is connected to another mass. Here is the equation of motion.
Here is the python code
trinket.io/glo...

[@pseudolullus]

I really love the fact that you add simulations and the code. I like playing with the parameters and the code on my own, it adds more to the learning imo.

[@alidogramaci7468]

Thanks!

[@DotPhysics]

Thanks for your support!

[@fizixx]

This was a lot of fun!

[@theunlimitededitor9538]

Watching the complete series... Loving it Keep up...

[@DotPhysics]

thanks! Glad you like it.

[@adityasagarshukla4912]

Love your videos keep doing it Sir❤️

[@DotPhysics]

thanks!

[@ajejebrazor4936]

Amazing! Is so so fascinating. Can I ask you to attempt a comparison problem with real results? Otherwise can I ask you to attempt different balls in slightly different conditions at once? Otherwise a graph showing the “state” space of the solution? Sorry but I’m really loving this series on Lagrangian mechanics

[@darkrick1638]

I liked to much, thanks

[@IBViRUS]

for more constant angular momentum you could try to use RK4 scheme. It might be a mess to implement. Euler's method is worst by errors it's produce for given time step. RK4 on other side gives exact values for quadratic function for example and over all gives much more accurate results.

[@DotPhysics]

yeah - that's a good point.

[@PulseWatchNews1]

I wonder whether when the mass on the table is moving (rotating) around the table will not that impose rotation on Z axis?

[@user-bm3ur8cz7e]

Nice video

[@DotPhysics]

thanks!

[@frogstud]

Wait, i count 1 more dof because there is nothing constraining the hanging ball except the string. Using rotational symmetry would allow one to reduce the dof by one imo

[@omwadekar8639]

What softwares you use to record the video (the black screen where u also solve equation s)

[@jorgedaniel1653]

I’m currently trying to create my own 1D Finite Element Analysis tool in Python. That way, I can learn Python and apply what I have learned from FEM, any advice on references I should use?

[@jorgedaniel1653]

I know it’s kind of random but I really enjoy seeing these problems and looking to incorporate numerical solutions to them. Hope to see more of it 🫡❤️

[@DotPhysics]

Here's something that might help - modeling a wave on a string with a bunch of masses connected by springs. kzbin.info/www/bejne/r6PcmKKFm9OfopY

[@godphysics2473]

The audio quality is too low, but apart from that Great!

[@DotPhysics]

I had a mic issue - but I think it's fixed for future videos. Sorry about that