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test Ameba test


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  • 4 months later...
  • 4 weeks later...

















[math]123.45\cdot a[/math]






test 6...










[math]a \cdot b \cdot c[/math]

















[math]{abc}_{d ef}[/math]


test 13...


[math]a b /c[/math]


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




[math]a _{b }+3.1 \cdot {10 }^{-12}[/math]


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




[math]3 \frac{x }{y }[/math]


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




[math]2 \sin x \cos y[/math]




[math]2 \, \mathrm{sin }\, x \, \mathrm{cos } \, y[/math]


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


test 18..


[math]a \bar{b }c[/math]


test 19...


[math]x \mathbf{y }z[/math]




[math]a b \mathtt{c }\delta \mathcal{Y } [/math]


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


matrix test1...


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


limes test1...


[math]\lim _{x \rightarrow \infty }\left( x +1 \right)[/math]



underline/overline test....


[math]\underline{a b}\overline{c d}[/math]


sqrt test...


[math]\sqrt{x }\sqrt[3 ]{y }[/math]


'd' test...


[math]d x[/math]


(PN: what about partial derivation sign??)

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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

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


This clearly hits problems when r=2M - ie at the Event Horizon where [latex]g_{tt}[/latex] becomes zero and [latex]g_{\tau \tau}[/latex] 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...

[latex]\frac{d^2\theta}{dt^2} + C\frac{d\theta}{dt} + \kappa\theta = \tau(t)[/latex]

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

[latex]f_n = \frac{\omega_n}{2\pi} = \frac{1}{2\pi}\sqrt{\frac{\kappa}{I}}\,[/latex]

Therefore, the period is represented by:

[latex]T_n = \frac{1}{f_n} = \frac{2\pi}{\omega_n} = 2\pi \sqrt{\frac{I}{\kappa}}\,[/latex]

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

[latex]\theta = Ae^{-\alpha t} \cos{(\omega t + \phi)}\,[/latex]


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

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  • 3 years later...
35 minutes ago, EdEarl said:


What am I doing wrong?

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

[math] \Delta [%math]


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


Edited by Mordred
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