Lagrangian Mechanics | Spring Mount Pendulum (with Python and sympy)

A pendulum is mounted to a point that has a vertical moving spring. What is the equation of motion?

Here is the code for the animation

[ChaineYTXF]

this is gold. thank you immensely for sharing

[teenspirit]

You can easily call this "physics for coders" because it is a very good example of going from differential formulas to numeric calculations.
Thanks, by the way.

[bendunselman]

It would be nice to have some phase space plots for some interesting values of k and R. And maybe a waterfall plot of the spectrum of the waveforms. And maybe add some dissipation.

[smalltimeprepper]

I doesn't hurt to go over it again says the best professor

[smalltimeprepper]

You should be a hand model! Thanks for making this im glad i found you.

[Electromowls]

" The total energy is constant so I am pretty happy " :)

[jtong]

Need help.

import sympy as sp

t = sp.symbols('t')
theta = sp.symbols('theta', cls = sp.Function)
theta = theta(t)
theta_dot = sp.diff(theta, t)
theta_dot

After running, it does not show anything at all. So, I add print(theta_dot)
It shows something like' Derivative(theta(t), t) ' instead of d(theta)/dt.

[fizixx]

Hey, excellent! I like colabs, and I haven't experiments with the symbols yet. Something to look forward to. :)

[marcrindermann]

doesn't vpython have a helix? would be so much nicer for a spring ;)

by the way, sp.diff(L, thetadot, t) also does what sp.diff(sp.diff(L, thetadot), t) does and in my opinion it takes nothing away from the readability, on the contrary, I think it's clearer to see what it does.