Recent content by yukcream

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 =...

Pervect you really very clever! Yep ~ What i mean is the past exam paper!:smile: yukyuk

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

what will be the result of \mathbf{v}\cdot\mathbd{a}? will it be zero as velcoity and acceleration are orthognal to each other!

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