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/sci/ - Science & Math

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7384303 No.7384303 [Reply] [Original]

Can someone explain to me how the graph of cosh can be so representative of the real world physics of supporting an arch or hanging a chain?

>> No.7384307

and also then, what would sinh represent?

>> No.7384318

>>7384303

It's a curve. So are arches and hanging chains.

They don't "represent" anything other than a ratio. Did you flunk highschool math or something?

>> No.7384337

>>7384318
no im in 4th year engineeering and this is the first time ive even heard of sinh and cosh

>> No.7384379

>>7384318
Terrible explanation, terrible social skills. Learn how to talk to people faggot
>>7384303
I believe it's due to the fact that if you consider all the forces acting on the rope and make a differential equation out of it the solution is a hyperbolic function. I am also interested to know the details however, never really studied those functions
>>7384337
I am concerned that you've been in university 4 years and have only just heard of hyperbolic functions. I never went to university and even I have heard of them.

>> No.7384385

>>7384379
So would sinh represent a solution to a differential equation that modelled real world behavior?

I'm more or less not asking "why" it works, but rather why the two phenomena are related

>> No.7384402

>>7384385
Yeah.

>> No.7384429

>>7384337
What sort of engineer are you friend?

>> No.7384433

>>7384429
electrical

>> No.7384435
File: 113 KB, 842x373, Morin 1-9.png [View same] [iqdb] [saucenao] [google]
7384435

This is considered a difficult question in an honours Classical Mechanics course, you might want to attempt it OP

>> No.7384440

>>7384435
i dont know how to do this

>> No.7384446
File: 130 KB, 612x716, pt1.png [View same] [iqdb] [saucenao] [google]
7384446

>>7384440
You know what, I think I'll just give you the solution. It'll explain to you EXACTLY how cosh is representative of a hanging chain. Some experience in solving differential equations and CM will help.

>> No.7384447
File: 137 KB, 667x783, pt2.png [View same] [iqdb] [saucenao] [google]
7384447

>>7384446

>> No.7384448
File: 87 KB, 576x475, pt3.png [View same] [iqdb] [saucenao] [google]
7384448

>>7384447

>> No.7384453

>>7384446
>>7384447
>>7384448
i see now thanks
so what could sinh possible represent then?

>> No.7384456

>>7384453
Huh, that was quick, thought it would take you a little longer to digest. Well sinh is just a function like cosh, in fact sinh can just as easily be used to represent the function of the chain by using identities. In fact right at the end of pt3 the function of the chain contains sinh.

>> No.7384458

>>7384456
so the graph of sinh doesn't represent anything

what im asking is akin to why does a sin curve represent some waves

>> No.7384460

>>7384458
I'm starting to have a feeling that you're getting the wrong idea about the hyperbolic trigo functions, they don't have to physically 'mean' something, and they are not unique to specific situations. They just happen to to be convenient representations of certain Physical situations, in fact if you were to do a lot of Physics problems you will encounter them many many times

As for your question about why the sin curve represents some waves, a lot of times you will realise that many waves in fact DON'T conform to sin or cos exactly, which is why we have fourier analysis to represent them approximately as infinite series of sin and cosine. We choose sin and cos because they are periodic functions, not because they are special in any regard, many functions satisfy the wave equation.

>> No.7384463

>>7384460
ok thanks my man

>> No.7384469
File: 44 KB, 747x165, cosh.png [View same] [iqdb] [saucenao] [google]
7384469

>>7384463
No problem.
Maybe you'll like to learn a little more about differential equations, you will see trigo and hyperbolic trigo functions come out sometimes. Even for a question as unassuming as pic related is easier to solve with some experience with cosh and sinh

>> No.7386148

>>7384318
>highschool
> cosh
priceless

>> No.7386158

sin and cos are the solutions to f''(x) = -f(x)
sinh and cosh are the solutions to f''(x) = f(x)
also sin(ix) = i*sinh(x), cos(ix) = cosh(x)
there's some weird shit with hyperbolic geometry but that's all there is to them really.

>> No.7386168

>>7384433
>4th year EE
>hasn't had hyperbolic function
We had them in sixth form, you must go to a literal shit hole of a school.

>> No.7386365

tanh is speed in function of time of a falling object (with air resistance).

>> No.7386373

>>7386168
>sixth form
Further Math huh? Wish my country offered something like that, but we don't, so I just went and studied Mechanics for olympiads instead.

>> No.7386377

>>7384447
>>7384446
>>7384448
Ok, so this problem has kept me up some nights. How on earth does one go from (1.41) to (1.42). I can follow how they derive the differential equation I just can not for the life of me solve that integral.

>> No.7386378

>>7386377
https://en.wikipedia.org/wiki/Logarithmic_derivative

>> No.7386412

>>7386373
There is no such thing as "further math". It's "further maths"

>> No.7386415

>>7386378
Thanks, I did see the log, but it's looks a little more involved than that

>> No.7386420

>>7386412
Alright mate, didn't know that.

>> No.7386424

What you're really asking is "How are the forces on a hanging chain different from that on a projectile"? And the answer to that is: a projectile only has the downward force mg on it, while every point on the catenary has a downward force mg, plus a leftward tension, and rightward diagonal-up tension.

>> No.7386480

>>7384337
Lol do you own a scientific calculator
I think engineering majors should own a couple or even a graphing calc

>> No.7386486

>>7386412
Hey you, fucktard. Tell me, is mathematics a plural? Mathematics are a cool subjects eh? If not drop da fokin ass.

>> No.7386507

https://en.wikipedia.org/wiki/Catenary

>> No.7387057

>>7386158
/sci/ challenge:

Prove A*cosh(x) + B*sinh(x) is the only solution to
f''(x) = f(x), f(0) = A, f'(0) = B

>> No.7387068

>>7387057
/sci/ challenge part 2;

Prove that the distance along a radial line of f(x) = cosh(x) to the x-axis is always exactly equal to the radius of curvature at this point

>> No.7387070

>>7387057
>>7387068
BTW guys these are FP3 questions from UK high school exams, so you should be able to do them

>> No.7387072

>>7384446
>not using Euler-Lagrange equations to minimise potential energy
Pls.

>> No.7387078

>>7387057
>>7387068
These are easy.

>> No.7387085
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7387085

>>7387078
Correct, they are very easy (high school) but I was wagering that the majority of /sci/ can't do them because they are first year comp sci majors who can't into mathematics

>OP is 4thh year EE ND hasn't heard of hypobolic trig functions

>> No.7387126
File: 117 KB, 372x351, 1381690451486.png [View same] [iqdb] [saucenao] [google]
7387126

Use Bessel functions for the Hanging Chain instead fucking pleblords

>> No.7388512

>>7387057
>>7387068
Solved both but the first used techniques I only saw in 1st year undergrad, do they really tech this stuff in UK high school??