Hyperbolic functions

Idan Tal shared this question 3 years ago
Needs Answer

Hi,


Can someone tell me how can I make this animation (file attached) with hyperbolic functions in Geogebra?


Thanks,


Idan

Comments (10)

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The catenary function should be manipulated through a slider (t) and any desired parameter, here a=10t/cosh(4), as per attachements.

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Be aware! The horizontal position of the chain can"t be reached, due to function degeneration into the line y=1.

Cheers

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Thanks, but I want this chain keep the same length always (for example: length=5) and when A' and B' are 5 grids away from each other, the chain should look like a segment.

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  1. I want this chain keep the same length always

this is very difficult but I will try

meantime I did an approx work

the lenght is near 4

it is undefined when C is (0,0) but this can be solved with if[] comand and segment

I think the original is approx also

Files: foro.ggb
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Thank you very very much mathmagic!!! You are great!!!


Please let me know if you made it perfect (exactly 4).

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have you enough with this trick?

four new objects seem to solve the problem

I dilated the objects of previous work for length=4

I did not get solution with integral equations

Files: foro.ggb
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Could you please re-issue the sheet without animation, but showing the point to move manually (via mouse)? I've faced the drawback shown below. Thank you

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the animated point is C . C is hidden. download the worksheet and "desanimate" C

show C and hide C'_1. both are near

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new worksheet using the general catenaria f(x)= 1/a cosh(a x) because the lenght is calculated =1/a sinh(a x)

the only approx calculus is for solving equations

https://www.geogebra.org/m/UYxnWced

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Awesome!!!

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...the general catenaria f(x)= 1/a cosh(a x) because the lenght is calculated =1/a sinh(a x) ...


Sure! This is a valid property of catenary. Further comments below

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