To physics monkey,
Thanks for your help but i cannot understand what you mean? how can i write out the relation between the damped period and undamped~ quite confusing !:frown: Also why I start by evaluating the damping factor after n periods and setting it equal to 1/e?
yuk
if the amplitude of a damped oscillation is decrease to 1/e after n periods, how can i show that the frequency is about [1-(8pi^2n^2)-1]times the frequency of undamped ocillations? can i assume that the oscillation is critical damping such that the term b/2m and k/m can be cancel in the...
I think my answer is correct~~
as z is only a function of coordinate x^i , derative of z wrt x^j & x^k will be zero ~ right? Do I make the mistake there?
Once more question is :
Given a fame S' which is falling along -z-axis with constant acceleration in an inertial frame S. Find a form of metric in the S' frame, assume in Newtonian approximation of the absolute time (t=t').
I just know a definition that
a = sqrt(g_ij dx^idx^j) but how...
To jimmysnyder:
Hope I can understand what you mean~~
I work out the steps, am I correct?
\Gamma^m{}_{ij} = \frac{1}{2}g^{km} (-g_{ij,k}+g_{jk,i}+g_{ki,j})
\Gamma'^m{}_{ij} = \frac{1}{2}g'^{km} (-g'_{ij,k}+g'_{jk,i}+g'_{ki,j})
\Gamma'^m{}_{ij} = \frac{1}{2}e^{z(i)}g^{km}...
Q1 If given a 2D Riemannian space, ds^2 = dx^2 + x^2dy^2, do the componets of the metric tensor are these:
g_11 = 1, g_12 = 0
g_21 = o, g_22 = x^2 ?
In addition, I got a question from my lecturer:
Q2. 2 metrics, defined in a Riemannian space, are given by ds^2 = g_ijdx^idy^j
and ds'^2 =...
I am studying general relativity now and I want to collect some pastpaper about general relativity. Could you mind share yours with me? :blushing:
yukyuk
I have read an article it states that the time-component of 4 acceleration vector is zero, as in 4 velocity vector, v^{0}=v so a^{0}=0. But in fact it is not correct! It should be a non zero quality.
yukyuk
O~~~~I get it :biggrin:
The correct answer is this, right?
\delta^{i'}_{k'}=T^{i'}_{m}T^{n}_{k'}\delta^{m}_{n}
\delta^{i'}_{k'}=T^{i'}_{m}T^{m}_{k'}=\delta^{i'}_{k'}
This time the indices on both side is balance?!
thank you very much~~~
yukyuk
I want to prove that the given martix
U^k{}_i
is invariant under Lorentz transformation~ am I correct to prove in following way?
Express U in delta as its really a delta function~
\delta'^k{}_i=T^i{}_mT^n{}_k\delta^m{}_n
\delta'^k{}_i=T^i{}_mT^m{}_k so
=\delta^k{}_i
You both help me...
To Mortimer:
Thanks for your article but I hope to read an article more related to 4 acceleration as I get in trouble in writing out the component form of 4- acceleration vector~
yukyuk
Given U^k_i, the components of U is a delta function i.e for i=k U^i_k =1,
to prove it is invariant under Lorentz transformation~~
I don't know how to express it in Einstein summation notation, I am very confused with the upper-lower index, is it right to write the transformation in this...
To Trilairian
I know it is too late to ask you, still hope you will answer this!
why a^o is zero? du^0/dt not equal zero ~ where t is the popertime~
why v^o = c? v^0 actually is 1/{1-(v^2/c^2)}
yukyuk