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/sci/ - Science & Math

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1046097 No.1046097 [Reply] [Original]

So i have a bet with a friend, he thinks /sci/ knows all when it comes to math/science. So i have a simple math question for you so that i can prove him wrong. Give me a function that can give a graph similar to the one i have drawn.

>> No.1046105

>So i have a homework for my professor,
Super cool story bro

>> No.1046106

LOGARITHM FAGGOT

OF COURSE, YOU HAVE TO ASSUME IT IS AN ORTHONORMAL GRAPH

>> No.1046103

Reported for homework thread

>> No.1046107

f(x)=-bx-ce^x+d

>> No.1046111

2s orbital radial function?

>> No.1046119

Morse potential, describes the potential energy of a 2-atomic molecule.<div class="math">
U(r) = D (1-e^{-a(r-r_0)})^2
</div>

>> No.1046132

>>1046111

Doesn't diverge at 0.

>> No.1046134

>>1046107
wrong.
>>1046103
>>1046105
if this were homework i could just look in the book and it would be in there somewhere, it is just a definition. it is a challenge to show that most people on /sci/ do not even know real math or science

>> No.1046135

So you want an asymptote at x=0 that converges to y=0 from below.

If I had remembered anything from Calc 2 I'd be able to help. Meh.

>> No.1046136

>>1046119
dont you mean a 2nd series atom?

>> No.1046139

>>1046134
NO YOU ARE WRONG

>> No.1046145

>>1046136
I don't know what you mean by a 2nd series atom (2nd period?), but the morse potential really is for diatomic molecules.

>> No.1046147
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1046147

>>1046107
using arbitrary values for the constants this is what you gave

>> No.1046153

>>1046145
my bad, yes 2nd period

>> No.1046157

>>1046147
NO YOU ARE NEGATIVE

>> No.1046163

How about...

f(x) = (1/2)^x/x

That's a start, I think.

>> No.1046180

1/x - 30*x*exp(-x)

>> No.1046186
File: 24 KB, 381x602, virtual-high-five.gif [View same] [iqdb] [saucenao] [google]
1046186

>>1046119
well, i guess i lose.
quite a bit faster than i guessed
and here i thought i had a substantially obscure function
have a virtual high five

>> No.1046189

1/x^12-1/x^6
or any different values.

>> No.1046192
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1046192

>>1046163
still fail

>> No.1046197

Just paste the image into the Wolfram Alpha search box like everyone else, homeworkfag

>> No.1046199

>>1046186
Morse potential doesn't diverge at 0 though, but you can easily add a <span class="math">1/x^3[/spoiler] to accomplish that.

>> No.1046201

>>1046119
>>1046186
Although, if you can tell me another application of the function ill give you 5 internetz.
Hint: think about space

>> No.1046205

>>1046197
I know the answer fag.
YOU guys dont seem to know the answer, except one guy so far, who only gave the easiest answer.

>> No.1046207

>>1046201
orbital distance.
duh.

>> No.1046227

>>1046201
I don't know any other applications for the Morse potential, but I do know that the effective potential of circular motion is not one one of them.

>> No.1046233

>>1046134
>>implying that /sci/ isn't made up of a collaborative of many anons, such as yourself.

>> No.1046237

Easy shit, it looks like the graph of potential energy so it must something like

<div class="math">-\frac{1}{x^n}+\frac{1}{x^n+1}</div>

>> No.1046241

>>1046233
>not disputing any point, in fact reinforcing my point

>> No.1046238
File: 68 KB, 941x755, 4646434.png [View same] [iqdb] [saucenao] [google]
1046238

>>1046197
that would not even work. the suggestion interested me so i tried. this is the result

>> No.1046244

>>1046237
did you mean x^{n+1} ?

>> No.1046247

>>1046237

goddamn latex

<div class="math">-\frac{1}{x^n}+\frac{1}{x^{n+1}}</div>

>> No.1046250

>>1046106
HEY IF I TURN ON CAPS LOCK MAYBE MY RETARDATION WILL SEE RIGHT.
that is nothing like logarithmic functions, orthonormal or not

>> No.1046261

>>1046237
>>1046244
>>1046247
not even close

>> No.1046275

Fourier to the mother fuckin series/transform.

You can write pretty much anything as a function, just depends on how many terms of the series you choose to include

>> No.1046288

Sci thinks global warming is anthropogenic even though only 0.03% of the atmosphere is CO2 and only 5% of it is man made. So no, sci doesn't know everything.

>> No.1046294
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1046294

<div class="math">f(x)=-x^{-1}\ln{x}</div>
seems easy enough

>> No.1046302

>>1046134
> it is a challenge to show that most people on /sci/ do not even know real math or science

knowing shapes of functions means knowing math? get a clue nerdo

>> No.1046323

-ln(x)*e^(-x)

Will give you that shape.

It's always negative after x > 1 and approaches 0 as x goes to infinity

>> No.1046331
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1046331

>>1046261

Theres a shitload of functions with that look

There answer is the functions that represent the total energy in an orbit

Circular orbit:

<div class="math">Energy= \frac{1}{2}mv^2-\frac{GM}{r}=\frac{1}{2}m(\frac{L^2}{m^2r^2})-\frac{GM}{r}</div>

L is angular momentum, so now we have E in terms of r

GM is huge so it'd look like this, pic related

>> No.1046356

>>1046331
FINALLY AN ANON CAN GETS IT

>> No.1046380

>>1046197
>>1046134
>>1046105
>>1046103
you whine about homework threads yet post in them?
>does not understand the idea of bumping

>> No.1046522

Vertical asymptote at 0.
Horizontal asymptote at 0.

Let <span class="math">f(x)=g(x)-h(x)[/spoiler]
<span class="math">\lim\limits_{x\to 0^+}g(x)=\infty[/spoiler]
<span class="math">\lim\limits_{x\to 0^+}h(x)=L[/spoiler]
<span class="math">\lim\limits_{x\to \infty}g(x)=\lim\limits_{x\to \infty}h(x)[/spoiler]
<span class="math">\exists a\in (0,\infty),\ g(a)-h(a)<0[/spoiler]

I'll go with <span class="math">g(x)=x^{-n},\ n>1[/spoiler] and <span class="math">h(x)=\csch{x}[/spoiler]. So <span class="math">f(x)=x^{-n}-\csch{x}[/spoiler] Sure, it peaks above <span class="math">f(x)=0[/spoiler] instead of approaching it from below like the graph weakly suggests, but the problem was just to make one that resembled it.

>> No.1046525

>>1046522
f(x)=x^{-n}-csch{x}

>> No.1046550

Vertical asymptote in 0, horizontal in infinity, negative after 1 for example, null derivative at 5, logarithmic growth after... should be plenty of this in your usual highschool manual.

>> No.1048041

look up a lennard jones potential

learn some useful shit

>> No.1048054

>>1046119
Pauling and Wilson... I love it.

>> No.1048073

>>1046097
Energy well for a proton approaching nucleus.

>> No.1048087

>>1048073
(negative)

>> No.1048090

An underdamped mechanical system would have a shape of this sort.

Potential, as has already been noted, would also give a shape like this.

I.e., nice try OP.

>> No.1048104

>>1048090
Underdamped? Wouldn't an underdamped system oscillate?
I think you mean critically damped.

>> No.1048119

>>1048104
I think you may want to look it up. You're thinking of undamped. :)

>> No.1050189

>>1046097
google it: Lennard-Jones potential
V(r)=4e( (s/r)^12 - (s/r)^6 )
used for pauli repulsion and van der waals force

>> No.1050248

>>1046119

WIN

>> No.1050260

>>1050189

Someone's been reading Wikipedia, because it says that there, and it's wrong - The L-J potential doesn't model Pauli repulsion.