[&+-]

Edited June 16, 201312 yr by EdEarl

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

 

LOL

 

 

test1...

 

[math]a[/math]

 

test2...

 

[math]{a}[/math]

 

test3...

 

[math]123a[/math]

 

test4...

 

[math]123.45\cdot a[/math]

 

test5...

 

[math]123.45\cdota[/math]

 

test 6...

 

[math]123,45a[/math]

 

test7...

 

[math]abc[/math]

 

test8...

 

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

 

test9...

 

[math]a_b[/math]

 

test10...

 

[math]{a}_{b}[/math]

 

test11...

 

[math]a_{b}^{c}[/math]

 

test12...

 

 

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

 

test 13...

 

[math]a b /c[/math]

 

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

 

test14...

 

[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)

 

test15...

 

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

 

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

 

test16...

 

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

 

test17...

 

[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]

 

test20...

 

[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??)

 

(PN: what about partial derivation sign??)

 

[latex]\partial x[/latex]

 

[latex]\partial x[/latex]

Thanks.

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

Edited December 10, 201312 yr by EdEarl

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

[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]

where:

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

\Delta

What am I doing wrong?

Edited January 29, 20187 yr by EdEarl

35 minutes ago, EdEarl said:

\Delta

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]

[math]\Delta[/math]

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

 

Edited January 29, 20187 yr by Mordred

ty

 

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