# test Ameba test

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Edited by EdEarl
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• 4 months later...

[acr=Laughing Out Loud]LOL[/acr]

LOL

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• 4 weeks later...

test1...

$a$

test2...

${a}$

test3...

$123a$

test4...

$123.45\cdot a$

test5...

$123.45\cdota$

test 6...

$123,45a$

test7...

$abc$

test8...

$a \cdot b \cdot c$

test9...

$a_b$

test10...

${a}_{b}$

test11...

$a_{b}^{c}$

test12...

${abc}_{d ef}$

test 13...

$a b /c$

(PN: not enoguh space between variables 'a' and 'b')

test14...

$a _{b }+3.1 \cdot {10 }^{-12}$

(PN: minus sign is a bit too long and exponent should be placed a bit higher)

test15...

$3 \frac{x }{y }$

(PN: too much space between fraction line and numerator/denominator)

test16...

$2 \sin x \cos y$

test17...

$2 \, \mathrm{sin }\, x \, \mathrm{cos } \, y$

(PN: I had to add \, space to make this look nice)

test 18..

$a \bar{b }c$

test 19...

$x \mathbf{y }z$

test20...

$a b \mathtt{c }\delta \mathcal{Y }$

(PN: \mathcal{} works with uppercase letters only)

matrix test1...

$\left[ \begin{array}{ccc}s & b & c \\ x & y &z \\ a & & \end{array} \right]$

limes test1...

$\lim _{x \rightarrow \infty }\left( x +1 \right)$

underline/overline test....

$\underline{a b}\overline{c d}$

sqrt test...

$\sqrt{x }\sqrt[3 ]{y }$

'd' test...

$d x$

(PN: what about partial derivation sign??)

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(PN: what about partial derivation sign??)

$\partial x$

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$\partial x$

Thanks.

Please forgive me, I copied a post to get some examples and did not remove the questions and comments.

Edited by EdEarl
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• 1 month later...

You have mentioned time and time again that there is a singularity at the event horizon - this is an artifact. Your argument from post one, repeated many times and even spelled out in post 29 (sorry my post numbers might not match as I see all posts) relies on the fact that r_s/r will become the root of a singularity.

The Scchwarzchild Spacetime Geometry can be represented as follows

$ds^2 = -(1-2M/r)dt^2+\frac{dr^2}{1-2M/r}+r^2(d \theta^2+sin^2 \theta d\phi^2)$

This clearly hits problems when r=2M - ie at the Event Horizon where $g_{tt}$ becomes zero and $g_{\tau \tau}$ becomes infinite. This was originally thought to be evidence of a physical singularity at the EH - but Eddington showed that it was merely an artifact of the coordinate system being used - ie Schwarzchild Coordinates

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• 2 weeks later...

$\frac{d^2\theta}{dt^2} + C\frac{d\theta}{dt} + \kappa\theta = \tau(t)$

If the damping is small, $C \ll \sqrt{\frac{\kappa}{I}}\$,, as is the case with torsion pendulums and balance wheels, the frequency of vibration is very near the natural resonant frequency of the system:

$f_n = \frac{\omega_n}{2\pi} = \frac{1}{2\pi}\sqrt{\frac{\kappa}{I}}\,$

Therefore, the period is represented by:

$T_n = \frac{1}{f_n} = \frac{2\pi}{\omega_n} = 2\pi \sqrt{\frac{I}{\kappa}}\,$

The general solution in the case of no drive force ($\tau = 0\,$), called the transient solution, is:

$\theta = Ae^{-\alpha t} \cos{(\omega t + \phi)}\,$

where:

$\alpha = C/2I\,\omega = \sqrt{\omega_n^2 - \alpha^2} = \sqrt{\kappa/I - (C/2I)^2}$

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• 3 years later...

\Delta

What am I doing wrong?

Edited by EdEarl
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35 minutes ago, EdEarl said:

\Delta

What am I doing wrong?

You need to place $on each side in the latter half so I don't activate the command tags replace the % with a / [math] \Delta [%math] [math]\Delta$

You will need to refresh the page to see if it worked as well

Edited by Mordred
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ty

I see, the preview button when replying does not do math.

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