General Definition and 1000 Threads

Homework Statement The general wave equation can be shown as: y(x,t) = ymsin(kx-ωt) Homework Equations See above The Attempt at a Solution My question relates to the variables present in this equation. I understand what the amplitude is, its the magnitude of the maximum displacement of...

Now, I am reading Carroll's http://arxiv.org/abs/gr-qc/9712019. On a page 88 he defines basic vectors, which are orthonormal (3.114) and basic vectors given by gradients of coordinate functions. Are these later basis vectors not obviously orthonormal?

Homework Statement If ##u(x,t)\in \mathbb R, x\in[-\pi,\pi] ## represents a standing wave with ##u(\pm\pi,t)=0## Then what is the most general solution u(x,t)? Homework EquationsThe Attempt at a Solution [/B] Using the separation of variable technique: u(x,t)=P(x)Q(t) I get ##P(x)...

Homework Statement hello all, I'm in the middle of solving a d.e using the series method. I have come across a weird pattern in part of my solution that I'm confused about: 6, (6)(10),(6)(10)(14),(6)(10)(14)(18),... Homework EquationsThe Attempt at a Solution I can see its 2(3), 2(3)*2(5)...

Hello, I have a conceptual problem. How can both General Relativity and a theory of Quantum Gravity simultaneously exist? GR describes gravity as the curvature of spacetime, while QG is most likely a gauge theory. Furthermore, if gravity is indeed describedby particle interactions-what does...

Getting stuck on something I think that could be trivial. Maybe someone can see my mistake. consider the system: $x' = -2x + y$ and $y' = 2x - 3y$ a) Write the system in matrix form my solution $\overrightarrow{X} = (^x_y)$ so: $X' = (^{x'}_{y'})$ so $A = $ \begin{bmatrix} -2 & 1 \\ 2 & -3...

Homework Statement (1+x2) y'' + 2xy' = 0 in powers of x Homework Equations y'' = \sum_{n=2}^{\infty} (n-1)na_nx^{n-2} y' = \sum_{n=1}^{\infty} na_nx^{n-1} The Attempt at a Solution (1+x2) y'' + 2xy' = (1+x^2) \sum_{n=2}^{\infty} (n-1)na_nx^{n-2} + 2x \sum_{n=1}^{\infty} na_nx^{n-1}...

Consider the system $x'_1 = x_1 + 2x_2$ and $x'_2 = 3x_1 + 2x_2$ If we write in matrix from as $X' = AX$, then a) $X =$ b) $X' =$ c) $A =$ d) Find the eigenvalues of **A**. e) Find eigenvectors associated with each eigenvalue. Indicate which eigenvector goes with which eigenvalue. f)...

This is a question I have been playing with this week out of curiosity but I keep coming up against brick walls and unenlightening results. Given the equation of an ellipse, say $$ x^{2} - xy + y^2 = 2, $$ I would like to find the equation of the line which passes through the major axis. I...

Homework Statement (a) Find the FRW metric, equations and density parameter. Express the density parameter in terms of a and H. (b) Express density parameter as a function of a where density dominates and find values of w. (c) If curvature is negligible, what values must w be to prevent a...

I'm reading An Intro to GR, Hughston and Tod, it says that in GR the idea is that the geometry of st varies from point to point, represented by allowing the metric to vary over space-time. It uses a (+,-,-,-) signature and so ##proper time=ds^{2}##. It then makes the comment that proper time...

Force" F"is applied on M1 .Although force applied is not directly on M2,but it will also experience this force" F" via M1,right? But I don't think it is correct.Because it implies that no matter how big the force on M1,the net force on M1 will always remain zero.And there will be unbalanced...

Hey! :o Find the solution of the problem $$u_{tt}(x, t)-u_{xx}(x, t)=0, 0<x<\pi, t>0 \tag {*} \\ u(0, t)=0, t>0 \\ u_x(\pi ,t)=-u_{tt}(\pi ,t), t>0$$ I have done the following: We are looking for solutions of the form $$u(x, t)=X(x) \cdot T(t)$$ $$u(0, t)=X(0) \cdot T(t)=0 \Rightarrow...

Hi, This is overwhelmingly more of a maths problem than a physics problem, because it's all theoretical. I'll give some background to modle it incase the math's isn't enough. Say you've got a planar structure of thickness 'd', lying on the z plane. Also say the upper and lower surfaces are y = 0...

Hi all, I have an undergraduate degree in Physics, but I've since specialized in more environmental applications of Physics. I've taken a few quantum Physics courses as part of my degree, but, if I'm being honest, what I took from those courses was more of a mathematical view of the field, such...

In a previous thread, reference was made to an entertaining "defense" of relativity by Einstein, which can be found here: https://en.wikisource.org/wiki/Dialog_about_Objections_against_the_Theory_of_Relativity One of the arguments Einstein makes in this dialog is that the twin paradox can be...

In the light of this policy https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/ , is it now considered acceptable to teach relativity by starting out with Lorentz Ether Theory (LET) and its Newtonian time which appears to be...

Is there an easy description for all the real to real functions that are order-preserving? I can only think of linear functions

Find the general solution of the given differential equation. $y'' + 2y' + y = 2e^{-t}$ I understand how to do everything in the problem- but I do not understand how we are obtaining $y = At^2e^{-t}$? Is this just some formula I should memorize or how exactly am I supposed to guess or figure...

I'm trying to show that any unitary matrix may be written in the form \begin{pmatrix}e^{i\alpha_1}\cos{\theta} & -e^{i\alpha_2}\sin{\theta}\\ e^{i\alpha_3}\sin{\theta} & e^{i\alpha_4}\cos{\theta}\end{pmatrix} Writing the general form of a unitary matrix as U=\begin{pmatrix} u_{11} & u_{12}\\...

Hello, It's my first question here. So I'll try to give as much as information as I know Actually I am stuck with a problem of centre of mass derivation of a triangle with its base on the X axis and symmetric about it. The base is b and height is H As far as I know I have to imagine it as a...

Guys , i have just completed my high school (4 days back) and know just the basic maths and physics (only what was taught in school).I have a great interest in physics and want to become a researcher.I am free for 3-4 months (after which i will join a college for majors in physics) and in that...

Please be patient as I struggle with latex here ... Part 1 of the problem says to start with: $ \frac{\partial\bar{r}}{\partial{q}_{1}} ={h}_{1} \hat{q}_{1} $ and then to find an expression for $ {h}_{1} $ that agrees with $ {g}_{ij}=\sum_{l}...

When I deduct the the general form of wave equation, I noticed it has a second order partial derivative form. I am wondering why wave equation has a second order partial derivative form nor a first order partial derivative form?

I stumbled upon this video: which seems to claim that past present and future exist at the same time due to the fact that observes in different frames would not agree on the order of events. The video claims that there are frames in which Mozart is alive. I don't think that this is correct...

I'm going to be tutoring next semester and I need a good general chemistry book to review. I used an old copy of zumdahl during general chemistry(not assigned text but worked fine) but I want a fresh look at the subject that is a little more rigorous mathematically especially. After a year of...

Hey guys I am in intro physics in college and took physics in high school. I have a general question about work/energy. In high school we used work= change in total energy and total energy = PE +KE +Q (Internal) which =work. In class there was a problem that read 2.00 kg block is attached to a...

Hello everyone, I'm studying some applications of AdS/CFT and I came across an expression of the Maxwell field written in the following way: $$ A=A_t(r)dt+B(r)xdy. $$ How does this notation work? Is it simply a way of writing the four-vector? If so, why do we use this notation? Thanks a lot!

Homework Statement In the normal loop the loop problem involving rotational energy where the marble goes down the hill and goes through a loop the loop, it asks for the minimum height of the hill to keep the marble on the track. Homework Equations But why does the normal force have to equal 0...

Homework Statement Solve for final Vout. Homework Equations Circuits The Attempt at a Solution So 1 and 2 are easy. I'm just going to skip to where I get confused. There is a 50k resistor between where I solved for Vout after the 2nd Op Amp. I found the voltage to be 12V. Now the solutions...

I know that the reduced mass, μ, of an object is: \mu = \frac{1}{\frac{1}{m_1} + \frac{1}{m_2}} \mu = \frac{m_1 m_2}{ m_1 + m_2 } But is there a general formula (or a simplified expression) for finding the value of: \frac{1}{ \frac{1}{x_1} + \frac{1}{x_2} + ... + \frac{1}{x_n} } ? Thank you.

I'm completely lost here. I've got the cheat sheet of trig rules, but they don't appear to be helping me, I've watched a half dozen videos on each of cos sin and tan, and nearly all of them discuss the wrong topic. I don't want help on any single problem, but advice. How can I make sense of the...

\frac {dy}{dt} = y^3 + t^2, y(0) = 0 My teacher said this IVP couldn't be expressed in terms of functions we commonly know. I was wondering what the general solution is? Thank-you

Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the main frame. Suppose a particular city has 25 of these buses, and cracks have actually appeared in 8 of them. (i) How many ways are there to select a sample of 5 buses...

Hello, few days ago I took an exam in my honors physics class and believe I did not do as well as I did on the other exam. Last exam had a few computational problems and the rest were general solution problems. This recent exam had 8 questions that were all general solution problems as opposed...

I am supposed to take calculus next school year but I want to do some physics work over the summer. Can anyone provide me the the most common calculus problems in physics? I was thinking that derrivatives, integrals, limits, and infinate series would be the main ones but I am likely wrong.

By wave-guides I refer to the device with (perfectly) conducting walls that enclose EM wave inside. I'm reading this tutorial here http://farside.ph.utexas.edu/teaching/em/lectures/node105.html and found this interesting boundary condition for wave-guides: ##E_{\parallel} = 0## -- (1)...

Homework Statement Find the deflection of light given this metric, along null geodesics. Homework EquationsThe Attempt at a Solution [/B] Conserved quantities are: e \equiv -\zeta \cdot u = \left( 1 - \frac{2GM}{c^2r} \right) c \frac{dt}{d\lambda} l \equiv \eta \cdot u = r^2 \left( 1 -...

Homework Statement I performed a lab with a simple DC circuit. The circuit has 4 resistors (i.e. R1, R2, R3 and R4), which is the same as shown in the attached image. When the voltages across all resistors were added, they were higher than the source. How is this possible? The KVL rule states...

Homework Statement (a) Find the proper time in the rest frame of particle (b) Find the proper time in the laboratory frame (c) Find the proper time in a photon that travels from A to B in time P Homework EquationsThe Attempt at a Solution Part(a) [/B] The metric is given by: ds^2 =...

Find the general solution of the given differential equation.. $$(1+t^2)y' + 4ty = (1+t^2)^{-2}$$ I'm kind of confused here on what to do... Do I want to do something like $$e ^{\int4t} dt$$ and then multiply that through on both sides or do I need to do something different here..I'm not...

Homework Statement (a) Find matrix element ##M_{ij}## (b) Show that ##x^j## is an eigenvector of ##M_{ij}## (c) Show any vector orthogonal to ##x^j## is also an eigenvector of ##M_{ij}## Homework EquationsThe Attempt at a Solution Part(a) [/B] \frac{\partial^2 \Phi}{\partial x^i x^j} =...

I have reopened the General Discussion classics thread to see if you want to suggest threads to be included or just let it go away (unsticky it). https://www.physicsforums.com/threads/general-discussion-classics.42220/

I have studied most of the concepts of Newtonian mechanics and understood the calculations and derivations involving the concerned formulae. I have a basic knowledge of calculus (differentiation of products along with differentiation of trigonometric, logarithmic, exponential and implicit...

Hi, just curious: I saw a result that for the multiplicative group G:= {1,-1, i, -i } , "every homomorphism ## h: G \rightarrow G ## is of the form ## z \rightarrow z^k ## for some ##k \in \mathbb Z ##. I can show this is true by considering the image of a generator, but I was wondering if...

Homework Statement Find the general solution. Homework Equations y"+y=x2sin2x The Attempt at a Solution Characteristic equation would be: m2 + 1 = 0 So,m2 = -1 Therefore, m = i or m = -i. Complementary function would be : Asinx+Bcosx where,A and B are constants respectively. If I write...

Hello, Everybody! I'm new to the board, and am happy to have found you! I have six questions I can't seem to find the answers to, either in books or online -- yet I know the answers are out there! I'll post each question in a separate thread, and hope that someone who knows far more than I do...

Homework Statement Suppose you send an incident wave of specified shape, ##g_I(z-v_1t)##, down string number 1. It gives rise to a reflected wave, ##h_R(z+v_1t)##, and a transmitted wave, ##g_T(z-v_2t)##. By imposing the appropriate boundary conditions [see below], find ##h_R## and ##g_T##...

In considering special relativity as a limiting case of the general theory (without matter or curvature) the question arose as to whether the pseudo-riemann nature of the SR metric is actually an independant (essentially experimentally determined) assumption/property or derivable from the...

Is the General Formula of benzene and diacetylene the same?:nb):nb):nb)