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Russia ☭ forever (git.io/vOZo0)
Viacheslav N. Mezentsev |
 1 user thanked uni for this useful post.
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Originally Posted by: uni  Ctrl+Shift+K. Can we solve this task with SMath + Mathcad 
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Можно попробовать, если будет доступен оригинальный документ Mathcad. |
Russia ☭ forever (git.io/vOZo0)
Viacheslav N. Mezentsev |
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 429 Was thanked: 42 time(s) in 39 post(s)
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Можно попробовать, если будет доступен оригинальный документ Mathcad.  Pendulum-Spring.xmcd (160kb) downloaded 8 time(s).
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The definition of l(t) must be inside or above the Mathcad block Federpendel-block.sm (40kb) downloaded 14 time(s). |
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 429 Was thanked: 42 time(s) in 39 post(s)
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 429 Was thanked: 42 time(s) in 39 post(s)
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2 users thanked Razonar for this useful post.
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on 06/12/2023(UTC), on 06/12/2023(UTC)
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 429 Was thanked: 42 time(s) in 39 post(s)
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 429 Was thanked: 42 time(s) in 39 post(s)
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Why I have an error in this task? Help please! Pund-Spring.sm (16kb) downloaded 4 time(s).
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 429 Was thanked: 42 time(s) in 39 post(s)
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More simple task Pund.sm (12kb) downloaded 3 time(s).
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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 (14kb) downloaded 10 time(s). Edited by user 07 December 2023 12:50:19(UTC)
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2 users thanked mkraska for this useful post.
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on 07/12/2023(UTC), on 07/12/2023(UTC)
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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 (16kb) downloaded 12 time(s). |
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on 08/12/2023(UTC), on 08/12/2023(UTC)
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Your Mathcad Given/Odesolve ... solves via Maple. Verhulst solves wrt limits ... pretty advanced. Inst_Verhulst.sm (28kb) downloaded 3 time(s).
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The equations of motion, using Lagrange dynamics, from this post:  ElasticPendulum.sm (245kb) downloaded 8 time(s).Best regards. Alvaro. Edited by user 08 December 2023 11:16:00(UTC)
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2 users thanked Razonar for this useful post.
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on 08/12/2023(UTC), on 09/12/2023(UTC)
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Originally Posted by: mkraska 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 (258kb) downloaded 7 time(s).Best regards. Alvaro.
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on 08/12/2023(UTC), on 08/12/2023(UTC), on 08/12/2023(UTC)
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Have you seen this plot   Edited by user 08 December 2023 19:11:42(UTC)
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