Pendulum.sm (233 KiB) downloaded 29 time(s).

Ctrl+Shift+K.

Wrote

Ctrl+Shift+K.

Can we solve this task with SMath + Mathcad

Можно попробовать, если будет доступен оригинальный документ Mathcad.

Можно попробовать, если будет доступен оригинальный документ Mathcad.

Pendulum-Spring.xmcd (159 KiB) downloaded 28 time(s).

The definition of l(t) must be inside or above the Mathcad block

Federpendel-block.sm (39 KiB) downloaded 33 time(s).

My solution


Pendulum-Spring.xmcd (82 KiB) downloaded 22 time(s).

Animation needed

Simple pendulum + animation.

ODE Pendulum Copy.sm (103 KiB) downloaded 24 time(s).

Comparing with the usual elastic pendulum.





Ochkov elastic pendulum.sm (32 KiB) downloaded 33 time(s).

Best regards.
Alvaro.

See please the Fig. 4.10 here
http://twt.mpei.ac.ru/ochkov/Ochkov-V-F-Engineering-Calc.pdf
Now I would like to rewrite this Russian-English book with SMath. Help me please!

Why I have an error in this task? Help please!
Pund-Spring.sm (15 KiB) downloaded 22 time(s).

More simple task
Pund.sm (11 KiB) downloaded 25 time(s).

If F(t) is requested as result, you have to specify F'(t). k(F) is the tangential stiffness of the spring, the inverse of the tangential compliance.

Federpendel-NL.sm (13 KiB) downloaded 28 time(s).

More animations
https://community.ptc.com/t5/Mathcad/One-interesting-problrm-with-shue/td-p/635149
Let create it with SMath
Слабо?

In this version you can specify the initial force in the spring. The initial conditions for x and y are adjusted appropriately.


Federpendel-NL.sm (15 KiB) downloaded 31 time(s).

Your Mathcad Given/Odesolve ... solves via Maple.
Verhulst solves wrt limits ... pretty advanced.

Inst_Verhulst.sm (27 KiB) downloaded 21 time(s).

The equations of motion, using Lagrange dynamics, from this post:



ElasticPendulum.sm (244 KiB) downloaded 29 time(s).

Best regards.
Alvaro.

Wrote

In this version you can specify the initial force in the spring. The initial conditions for x and y are adjusted appropriately. ...

A comparison between Martin's solution and that given by the equations of motion obtained from the Lagrangian. Spoiler: both give the same result.

I'd like to point out how incredibly complicated this problem actually is, and what a series of brilliant implementations Martin makes. For example, where the hell does he get the time derivative of the force on an elastic bar when he is given only the length of the bar as a function of the force? Obviously, it is not enough to apply the theorem of the derivative of the inverse function, but you also have to have a deep knowledge of the mechanics of the system to remember something called tangential stiffness, and although it uses k to represent it, we forgive it because It's German and they are well known to use their own abbreviations. Well, actually I don't know what letter to use, because I don't remember ever using that magnitude for any practical purpose, but in Spanish literature it is quite common to use k for its inverse, which is the constant that appears in Hooke's law. Or at least I think so, because the existence of elastic bodies is actually a complication, they should all be rigid better.

Another notable thing about this example is that I would like someone to please explain to me how the hell the Viacheslav plugin manages to handle l'(t) within the equations, because I honestly didn't expect it.

Federpendel-NL - Lagrangian.sm (257 KiB) downloaded 37 time(s).

Best regards.
Alvaro.

Have you seen this plot