/sci/ - Science & Math

How about writing down the "extremely shit tier answer" correctly?
<span class="math">x(t) = k\ln{t}[/spoiler]

Initial conditions? Domain of k? Domain of x? Domain of t?

>>3406195
Are you an aspie or something?
You seem to be unable to help with anything unless you ask them exactly what they meant instead of just heuristically assuming you know.
Honestly. Is it just arrogance? You have to talk about math so you can show everyone how smart you are before solving something?
Do I need to post the peano axioms before I can get you to tell me what 1 + 1 is?

Christ almighty. Why are you here?

>>3406202
>2011
>hating on Josef

I seriously hope you don't do this.

Newtons law of gravitation...

>>3406211

the only "i seriously hope you dont do this" comment i've ever agreed with

Yay implicit differential equations.

Let's substitute: <span class="math"> a := x , p := x' , y'' = \frac{d x'} {d t} = \frac{d p} {d a} p [/spoiler]

Now solve your equation for p and then you can get x' from x'(t) = p(x(t)).

>>3406202
LOL. New to /sci/ aren't we? You can't just come in here, throw us some half-assed problem without a rigorous specification, and then complain that people will troll the hell out of you.

Go back crying to /b/, newfag.

>>3406202
Well in that case take this picture of a carefully selected crop of the solution that makes it completely useless, yet will show you in the end that I've been somebody who could have helped; together with a nice go fuck yourself.

>>3406223

That should be x'' not y'', my bad.

[ -6kt^2 + c]^(1/4) = x

>>3406227
>2011
>pretending to know shit about math

I seriously hope etc. etc.

>>3406202
you must be retarded. solutions aren't even the same if k/x >0 or k/x<0.
Now go eat a banana and get 0.1µSv of radiation

Its F=ma. Your potential is -k/x, energy:

<div class="math">\frac{1}{2}(\frac{\mathrm{d}x }{\mathrm{d} t})^2-\frac{k}{x}=C</div>

Now its separable. Could this work?

>>3406240

first day at sci

>>3406195
k is constant, x and t are all reals, I was assuming arbitrary constants for the initial conditions.
This is my first post in this thread other than the original post, I hope some of the ass hats in this thread didn't make you leave, I could really use your help.

>>3406196
That comes from:
<span class="math">
\frac{d^2x}{dt^2}=-\frac{k}{t^2}
[/spoiler]

>>3406202
>2011
>lacking rigour in any advanced math problem
I seriously hope you guys don't do this.

>>3406202
OP here... I really could have used Josef's help, I've seen his contributions in other threads and I know he is intelligent. You should seriously consider testing gravity laws using yourself and a cliff.

>>3406263
>x''(t) = -k/x(t)²
>x''(t)*x'(t) = -k*x'(t)/x(t)²
>x'(t)² = 2*k/x(t) + A (A is a constant)
>dx/dt = sqrt(2*k/x + A)
>dx/sqrt(2*k/x + A) = dt

Then t = f(x) where f is found here: http://www.wolframalpha.com/input/?i=1%2Fsqrt%282*k%2Fx%2BA%29

Find f^-1 and you're done.

>>3406263

As I said, use substitution. Continuing from my initial post, the dgl becomes:

<span class="math"> \frac{dp} {da} p = - \frac{k}{a^2} [/spoiler]
<span class="math"> \int p dp = \int - \frac{k}{a^2} [/spoiler]
<span class="math"> \frac{1}{2} p^2 = \frac{k}{a} [/spoiler]
Note: WLOG assume C = 0 .
With this you get:
<span class="math"> p = \sqrt{ 2 \frac{k}{a} } [/spoiler]

Now if we resubstitute this we get:

<span class="math"> \frac{dx}{dt} = \sqrt{ 2 \frac{k}{x}} [/spoiler]

Use seperation of variables to solve for x(t)

No one said it was gonna be pretty.

>>3406297

Yay! that is my solution >>3406252 for C=0!

>>3406297
I used wolfram|alpha... pic related (unfortunately)

>>3406321

Well at least you can find an algebraic solution, just because the initial equation looks simple doesn't mean it is.

we can assume that x(t)>0.
On the intervals where x'(t) !=0, you can multiply on both sides by x'(t)
x''(t)*x'(t)=-k*x'(t)/x²(t)
<=> d(x'(t)²)/dt=d(k/x(t)) /dt
<=>x'(t)²= k/x(t) + C
I'll think about the end

>>3406345
I'm actually not sure if this can be solved for x in terms of t. I can't do it and wolfram can't do it... doesn't mean it can't be done, just saying I don't think I'll find the solution today.

>>3406202
>>3406202
i know right.

>Why are you here?

that one is too easy, he loves /sci/ because it's full of high schoolers and undergrads meanwhile he's a grad student thus he loves the feeling of superiority. one thing i'll tell ya, he isn't here for the "science", as most threads here are either home works, religion discussions or layman subjects, if he were after real level discussions he would be at physicsforums.com, there we have 10 ph.d.s for every board, BUT he would be "just another grad student" there and even yet out smarted.

nothing personal joseph, i just don't live overall tripfags

OP here with a mostly unrelated question:

I really have no idea what I'm talking about here but... basically is there any way that I can distinguish myself from other anons so that fuck heads like >>3406202 can't derail my thread? I know I could just put OP in the name field, but that is pretty much just as easy to troll as being anonymous. I guess I'm talking about tripcodes? Like I said, I have no idea what I'm talking about.

>>3406429
http://www.4chan.org/faq#trip
there's everything you need to know!

Answer is (9k/2 * x^2)^(2/3)
/thread

>>3406386
I meant x'(t)²=2k/x(t) +C, sorry

>>3406429
why would having a trip disable people of derailing threads?

>>3406420
Seriously asshole, gtfo of this thread. I asked a legitimate question (not homework, btw, I'm a speech class and intro to music class away from my bachelors in physics, but I can't afford to finish right now, so I'm just curious and trying to get better at dif. equations) and the only thing you can contribute is making fun of people who are trying to help me. If you're so smart, why won't you actually help me understand how to solve this problem?

>>3406462

Your question has already been resolved by like 7 different anons so far.

>>3406444
lol, well now I feel kind of dumb for not just looking it up in the first place, but thank you anon!

>>3406461
basically, if I'm posting in someone else's thread, I'm going to stay anon, but if I make my own thread and someone decides to pretend to be the OP and starts making fun of people in the thread (case in point, this thread) then I have a defense against it

>>3406387

Well you're trying to find a very general solution, usually if you solve this kind of problem you're given boundary conditions that make it easier to solve. Don't forget if you do a definite integral with the substitution approach you integrate from a0=x0 to a and p0 = x'0 to p and later from 0 to t and from x0 to x.

Now why don't you assume x0=x'0=0 and try solving it again?

>>3406487
<span class="math">
x(t)=???
[/spoiler]
is the resolution... x as a function of t. This has not been found and no one was supplied a method that can actually find it. Find t(x)? yeah, I did that before I made this thread. You can't get x in terms of t from any of the methods described here.

>>3406519

Its pretty common for integrable dynamical systems to give time as a function of whatever instead of the other way around. Your problem is basically finding the solution for Newtons law of gravity in 1 dimension. You can use the conservation of energy and that yields a first integral which solves the problem.

>>3406519

Plot t(x) and flip the graph 90 degrees, theres x(t)!

>>3406508
If
<span class="math">
x_0=x'_0=0
[/spoiler]
then x(t)=0 (if k=GM, this is Newtons law of gravitation... lets say the earth is a point and you're at that point and not moving, you never move due to gravity), but I see what you're saying... I was really hoping to find a general solution though. :(

>>3406519

Well I guess if you're trying to do it very general then this goes past the limits of my knowledge, but i wouldn't let it bother me haha.

>>3406542
True, but the graphical solution doesn't help much when I'm trying to find the actual function x(t), not just the graph of <span class="math">t^{-1}(x)[/spoiler].

>>3406554
You're definitely right, I SHOULDN'T let it bother me, but unresolved math problems plague my soul. I won't rest until I find the solution (exaggeration of course, but I think we've all been there).

OP here again. I have to go to my brother's house to help him with some stuff, but I just wanted to apologize (even though it wasn't me) for the assholes ITT, and thanks to everyone who stuck with me and helped (especially anon of Germany).

>>3406582
"especially anon of germany"
that's the effect of tripcodes etc.
other people helped too.