Pendulum.sm (233,97 KiB) descargado 1472 vez(es).

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 (159,03 KiB) descargado 1491 vez(es).

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

Federpendel-block.sm (39,22 KiB) descargado 1462 vez(es).

My solution


Pendulum-Spring.xmcd (82,56 KiB) descargado 1501 vez(es).

Animation needed

Simple pendulum + animation.

ODE Pendulum Copy.sm (103,31 KiB) descargado 1467 vez(es).

Comparing with the usual elastic pendulum.





Ochkov elastic pendulum.sm (32,17 KiB) descargado 1430 vez(es).

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 (15,02 KiB) descargado 1477 vez(es).

More simple task
Pund.sm (11,53 KiB) descargado 1495 vez(es).

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 (13,71 KiB) descargado 1472 vez(es).

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 (15,06 KiB) descargado 1488 vez(es).

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

Inst_Verhulst.sm (27,14 KiB) descargado 1465 vez(es).

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



ElasticPendulum.sm (244,53 KiB) descargado 1460 vez(es).

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 (257,87 KiB) descargado 1596 vez(es).

Best regards.
Alvaro.

Have you seen this plot