Terms Definition and 1000 Threads

Dear Physics Forums denizens, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you...

We usually only consider the first order term for an oscillation, are there any papers on extending that model and including third and fifth order terms (since only odd power terms would cause a periodic motion)? The ODE would look like x''=-αx-βx^3+O(x^5)

Homework Statement How many terms are needed in the series 11+16+21+26...+ to exceed 450 d=5 Homework Equations Sn=n/2(2u1+(n-1)d) The Attempt at a Solution (455 because is term exceeding 450 by the d of 5) 455=n/2(22+5n-5) 455=17n+5n2 455/17=5n2 Calculator work, but...

Assuming $$\vec{r_{a}}$$ and $$\vec{r_{b}}$$ is calculated from an inertial frame of reference. then for any two objects (named a and b) in a system of more than two objects, Is this the Newton's third law, $$\frac{d^{2}}{dt^{2}}m_{a}\vec{r_{a}}=-\frac{d^{2}}{dt^{2}}m_{b}\vec{r_{b}}$$...

Hi, Referring to Jackson's Electrodynamics 3ed, page 197, line 5. He assumes that the magnetization can be divided into volume part and surface part, thus generating eqn 5.100. This is fine. In a straightforward way, I wanted to do the same but for electrostatics, eqn 4.32:∅= (1/4πε) ∫dv...

Can Someone Explain What String Theory Is? (Simple Terms With Examples) Ive been hearing a lot of references to this new string theory, what is it?

Homework Statement Consider the function φ(x) ≡ x on (0, l). Find the sum of the first three (nonzero) terms of its Fourier sine series. Reference: Strauss PDE exercise 5.1.3 Homework Equations The Attempt at a Solution I have found the coefficient without difficulty, it is...

The relative ordering of energy in the crystal field of d4 ions are arranged as 4A1g, 4T2g and 4T1g. How can I determine this? What is the rule for describe the relative energy of the terms for dn ions?

I have seen the derivation of the kinetic energy equation using F=M*v' and E=F*x And I can see how this works, however if you try to do this without thinking about velocity, and only thinking about the rate of change of distance, and the rate of change of rate of change of distance, then the...

-x^3+12x+16 Every single technique I read about online of how to factor 3rd degree polynomials, it says to group them. I don't think grouping works with this. I tried but it didn't work, since there's only 3 terms. Apparently I'm not supposed to have a cubic variable without a squared...

Given the formula \vec{p}=\frac{m_0}{\sqrt{1-\frac{|\vec{v}|^2}{c^2}}}\vec{v}, I'd like to make \vec{v} the subject, so I can do a numerical approximation for some relativistic motion problem. I want to treat it as a vector equation, but since it is non-linear, the only way I can think of is to...

Homework Statement from [-2,2] rad(4-x^2) Homework Equations The Attempt at a Solution I know its a circle and i get the equation to be y^2+x^2=4 and I believe it has to be divided into a circle and rectangle so the area of the rectangle i got to be 2 the circle i got to be...

Homework Statement Homework Equations Hooke's law. F = kΔx ω = sqrt(k/m) The Attempt at a Solution For part A F = mg = kΔx k = mg/Δx g is a constant so the spring constant is proportional to the mass and inversely proportional to the change in distance that the spring...

I'm beginning to study QM, and as I understand all the information we can get out of system with 1 particle is the probability distribution function (which has position and time as variables). By knowing the wave function it's possible to know the probability distribution function, but that's an...

Homework Statement 1.1!+2.2!+3.3!...n terms Homework Equations The Attempt at a Solution The first part of every term is in AP whose cd is 1. Also the nth term of this series is given as n.n! If I expand it it becomes n.n(n-1)(n-2)...1 Now S_n=\sum t_n \\ = \sum n.n(n-1)(n-2)...1...

Is power a quantity defined by: \frac{dU}{dt} and \frac{dW}{dt} Is it just defined to be it, or can it be derived in terms of the other (I mean, dU/dt in terms of dW/dt and vice versa)? I now there's physical motivation to it, but sometimes I just can't help trying to ponder how these equations...

The event horizon of a Kerr black hole is often depicted as being spherical, but this seems to be a reference to the horizon as defined in Boyer-Lindquist coordinates, where horizons appear at a constant value of r. However, Thorne describes the "black hole's horizon bulg[ing] out at its...

Is there a complex field that when properly interpreted yields the four components of electromagnetic vector potential, A_0, A_1, A_2, and A_3? Somewhat along the lines of the complex field ψ yielding information about a particles energy, momentum, and position probability. Thanks for any...

Homework Statement Click to enlarge Homework Equations K= 1/2 mv12 + 1/2mv22 p= m1v1 +m2v2 The Attempt at a Solution I have pages and pages of trying to simplify/work backwards and nothing is working!

Hi, All: Sorry if this is off-topic, but I did not know where else to ask. These are geometric/topological terms, so I thought it'd make sense to ask here: I am reading a math paper in French, and I'm having trouble : 1)Cellulation de Contact . Cellules. I suspect this has to see with...

Hi friends I want to solve an equation which is function of x,y,z,m but i want to find answer like this m=... i want my answer(m) to be a function of x, y, z but when i solve it in MATLAB or mathematica none of them give me the answer I know that my equation must have 4...

I have across the following argument, which seems wrong to me, in a larger proof (Theorem 4 on page 9 of the document available at http://www.whitman.edu/mathematics/SeniorProjectArchive/2011/SeniorProject_JonathanWells.pdf). I would appreciate if someone can shed light on why this is true...

What does "phase of the motion in terms of cosine displacement" mean? I'm getting tripped up on the wording of this homework question. Homework Statement Measured acceleration: An accelerometer has measured the simple harmonic motion shown in the image below. Homework Equations You...

The "cosmological" proper distance from the origin, D(t), to an object at radial co-ordinate r at cosmological time t is given by D(t) = a(t) r(t) The corresponding "cosmological" proper velocity v of the object is given by v = \frac{dD}{dt} = \frac{da}{dt} r(t) + a(t) \frac{dr}{dt} Using...

Homework Statement The continuity equation provides a second relation between the vA and vB, this time in terms of the diameters d and D. Numerical check: If the diameters are d = 1 cm and D = 10 cm, what is the ratio of the speeds, vB/vA? Homework Equations To clarify, is both d and D...

This problem is really making my head spin. I'm in university calculus II and my teacher loves giving us extra homework that is supposed to really challenge us. This is problem 1 of 5. "Let 0<r<R and x2+(y-R)2=r2 be the circle centered at (0,R) of radius r. Revolving the disk enclosed by that...

Why the heck will the sum of such a series going towards infinity change if its terms are re-arranged? My book omits the proof, and without it this claim makes no sense to me. Can somebody provide an example of such a series, and maybe some light explanation (I'm way too exhausted for heavy...

Hi guys I have 5 term which each term includes three function of time (autonomous system ), i want to obtain time derivative of each term as other terms for example if i define each term as a dimensionless variable , e.g. x , y , z , v , w , i want to know dx/dt = as a combination of x , y ...

I find the expression: "In general, one can expand the atomic displacements in terms of all the lattice wave modes (resembles a Fourier series expansion)" at: https://courses.cit.cornell.edu/ece407/Lectures/handout17.pdf But I have not found the expression in any other literature. (In fact...

Hello All, I am new to GR, studying slowly. I am little bit confused between the following terms and their usage: (a) Co & contra variant vectors - Do they help in transformation? (b) What is a co-ordinate free system? Do co & contra variant vectors help it? (c) What is parallel...

Homework Statement Let Sn = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}...+\frac{1}{n}. Show that |S2n-Sn|\geq \frac{1}{2} Homework Equations The Attempt at a Solution So I'm going to try and use induction Base case let n=1 |S2n-Sn| = \frac{1}{2} So true for base case...

I've been working on problems that deal with pendulums and I've noticed that a few of my answers require me to find the angular velocity, frequency, period of a pendulum. I managed to get the answer right every time, but there's a step that I didn't understand, namely converting angular...

I'm trying to keep a balance in difficulty next quarter and would appreciate some feedback as to the difficulty of these classes. The four I'm choosing between are Linear Algebra (upper division), Linear and Nonlinear Systems of Differential Equations, Ordinary Differential Equations, and...

Homework Statement "A satellite orbits the Earth in a circular orbit of radius r. If the orbital speed of the satellite is v, what is the orbital period T of the satellite in terms of v and r? You must explain how you derive the expression for the period."Homework Equations Speed =...

Please do your best to describe E=Mc^2 to me in the most plain English you know and as basic as possible without leaving out details. Any links you think would help would be great. Thank you

I graduated from high school this year and took the three main sciences (biology, chemistry and physics) as well as math up to Calculus. I've decided to take a year away from school for a couple reasons. But that doesn't mean that I must stop learning. Recently I bought a book which gives...

I was just reading an article on superstringtheory.com in the Black Holes section entitled "Space, Time, and String Theory" when I came across the following predicted reformulation of Einstein's tensor: The explanation for this was as follows: My question is this: are those correction...

Homework Statement Find Vo as a function of Vg and the open-loop gain A. Attempt I'm not sure what open-loop gain means. I redrew the circuit so it made more sense to me, but I'm still not getting it. It seems that Vo is the voltage across both RL and the 4k resistor. The...

Hello, I need your help in clarifying some points from Normal Distribution Theorem: What does this expression exactly says: P(Z<=z) ? Z is random variable? z is deviation?

I realized that one of my main problem is remembering terms like, whole numbers, rational numbers, etc. I was just wondering how important was it that I actually know these terms? I can do the math, just have problems with some of the terms.

Homework Statement Write down formulae for dX in terms of dA, dB, dC if: X = [(A) (B^2)] / C Homework Equations I'm using the formula below as this corresponds to this relationship. (dX/X)^2 = (dA/A)^2 + (dB/B)^2 The Attempt at a Solution For the first line, not the...

Homework Statement My book talks about the "reduction formulas" for evaluating trigonometric integrals by parts. However, is this the same thing as "recursive" formulas for integration by parts, a term which is not mentioned in my calculus book? Homework Equations The Attempt at...

Homework Statement I was given this problem as homework and managed to find the solution online, but I don't fully understand it. My only question, and the reason I was getting this problem wrong, is because I wasn't realizing that the functions evaluated from -∞ to +∞ were vanishing...

Homework Statement Is mass a conserved quantity under Special Realitivity? Homework Equations E=mc^2 The Attempt at a Solution Total energy is always conserved in an isolated closed system, and since mass is just another form of energy, then mass would be conserved in a...

Problem statement: Define isOdd function, and then define isEven function in terms of isOdd function. My attempt is ridiculous: var isOdd = function (x){ if (x % 2 ===0){ return isOdd; }else{ return "is even"; } }; var isEven = function (){ return; };

I have been tasked with solving the following inequality: \frac{1}{x} < 4 Attached to this thread is my attempted solution. As you can see I begin with simply solving the inequality for x, and I obtain the result x > \frac{1}{4} Next, I convert the equation into what I thought was the...

What exactly do the terms "near-field" and "far-field" mean? What exactly do the terms "near-field" and "far-field" mean (especially in the context of the two problems attached)? Other than the confusion about those terminologies, I fully get how to do these problems (1.1 and 1.2). Any...

Homework Statement Suppose P is invertible and A = PBP^-1. Solve for B in terms of A. Homework Equations (AB)^-1 = B^-1*A^-1 The Attempt at a Solution multiply from the left of each side of the equation by P^-1: P^-1 *A = BP^-1 Take the inverse of both sides: (P^-1*A)^-1 =...

Me and a friend was contemplating the ratio of even to odd number in Pascals triangle. After some thought we arrived at a ratio like this when looking at a triangle of 2k-1 rows. \frac{2^{2k-3}+2^{k-2}}{3^{k-1}} - 1 As expected, this ratio grows exponentially. (I.e. almost all numbers in...

In the paper http://arxiv.org/pdf/hep-th/9301028.pdf pages 8-9 Pullin shows how to write the Einstein action in terms of tetrads e^a_I. Part of the proof is: "...the last term yields e_M^{[a} e_N^{b]} \delta^M_{[I} \delta^K_{J]} C_{bK}^{\;\;\; N}. It is easy to check that the prefactor in this...