Analytical Definition and 260 Threads

Hi guys; I have an analytical solution for the deformation of a beam due to a couple with moments C_1 and C_2 with boundary conditions y=0 and x=±(L/2) where L≡length of the beam. The derivation from the Bernoulli-Euler equation is below: \begin{align*}...

Homework Statement For the system given, both objects have the same charge and same mass (both given). I'm also given string length, L. I need to solve for θ. Homework Equations Coulomb's Law, W=mg The Attempt at a Solution Using simple equilibrium force analysis (with weight, tension, and...

1. Here is the Problem: A line passes through A(2,3) and B(5,7). Find: (a) the coordinates of the point P on AB extended through B to P so that P is twice as far from A as from B; (b) the coordinates if P is on AB extended through A so that P is twice as far from B as from A. Homework...

Suppose that the Taylor series of a function ##f: (a,b) \subset \mathbb{R} \to \mathbb{R}## (with ##f \in C^{\infty}##), centered in a point ##x_0 \in (a,b)## converges to ##f(x)## ##\forall x \in (x_0-r, x_0+r)## with ##r >0##. That is $$f(x)=\sum_{n \geq 0} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^n...

Nowadays much of the community of astronomy and astrophysics is focused on simulations and data analysis. Thus people, who do not have access to grids and data, must resort to analytical analysis. What are the challenging areas of astronomy and astrophysics that rely on analytical workout rather...

Hello, I'm a second year physics student. We are going to use "hand and finch analytical mechanics", however the reviews I saw about this book are bad. I've already taken calculus for mathematicians, linear algebra, classical mechanics, special relativity, and electromagnetism. The topics it...

I wonder if there is an analytical solution to: b=a*x-θ - x with a>0, b>0, x>0, θ>1

Differential equation \begin{align} \frac{{\partial}^2 T (x,t)}{\partial x^2} = \frac{1}{\alpha}\frac{\partial T(x,t)}{\partial t}, \end{align} boundary conditions \begin{equation} \begin{aligned} T(x, 0) = T_\infty \\ -k\frac{\partial T(0,t)}{\partial x}= h(T_{max} - T(0,t)) \\...

At a certain instant, the velocity and acceleration of a particle ar defined by v= 3i + 4j - 6k m/s and a=-2i + 3k m/s2. Find the radius of curvature and change of speed of the particle at the instant.

Homework Statement Explain using word, diagrams, and/or calculations.. (1) Why must n always be <= 2d/λ? (2) If λ is significantly greater then d, why will no diffraction occur? Homework Equations Bragg's Law nλ=2dsinθ n has its maximum when sinθ is 1 (at 90°) The Attempt at a Solution I am...

Hi, I am struggling to understand the maths in the text shown below. (1) How does: r(t) = Acos(wt)+Bsin(wt) become; sqrt((A^2)+(B^2))cos(wt - arctan(B/A))? (2) He states that we can represent the input as a phasor and in one of three ways but doesn't say which one. (3) He then focus on the...

Hello everybody! I know how to solve Laplace equation on a square or a rectangle. Is there any easy way to find an analytical solution of Laplace equation on a trapezoid (see picture). Thank you.

the closed analytical solution of exp [((- i phi)/2) * h3] someone could help!

1.What are the mathematical prerequisites needed to grasp analytical mechanics conceptually and technically? 2.To understand the very concept of analytical mechanics, do I need to train my self in Euclidean and Riemannian manifolds, and do I need to have good knowledge in topology and...

I would like to prepare 50.0 g of 50 ppb Pb standard solution in 1% HNO3 gravimetrically, in a 50.0mL plastic tube from a stock solution of 50 ppm Pb. From what I understand, this is a dilution...so C1V1 = C2V2 I like working in mg/L more than ppb and ppm so I converted 50 ppb = 0.05 mg/L 50...

What's your take on preserving stamina/maximum mental capacity for quant and skipping the essays? I hear physics grad programs don't care at all, some don't even take the scores. Thoughts?

Hello guys! I have following differential equation mx"(t)+b(x'(t))x'(t)+k(p)x(t)=0. As can be seen, "attenuation term" is dependent of velocity x'(t). Also stiffness term k(p) is dependent of term p, which is p=k(p)x(t)/A. In this equation A is constant and k(p) means, of course, same term as...

Hi everybody! I'm very interested in the methods of complex analysis in theoretical physics. By these methods I mean such things (tools) as (for example) analytical properties of scattering amplitudes (or S-matrix) in QFT, regge calculus in QCD, analytical continuations of Einstein's equations...

So I'm taking analytical mechanics next semester. The textbook they use is Thornton and Marion's "Classical Dynamics of Particles and Systems". I want to learn it all this month. It is feasible, but extenuating. But there is another option. I could read Robert Fitzpatrick's Newtonian Dynamics...

Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...

Next semester I begin studying analytical mechanics. The book they use in class is Thornton and Marion "Classical Dynamics of Particles and Systems". I wanted to read something about this during the summer, and stumbled upon Lanczos' book " The Variational Principles of Mechanics". Lanczos'...

Maybe a little bit of a fresh mathematical virgin thing to ask, but what exactly is the definition of analytical geometry? I am asking for the reason I have recently acquired a book on the subject, but I found it by accident, and I would like to comprehend the most basic concepts of it! I am...

Hi i am working on a research paper for which i need very good citation for the analytic analysis coupling Electric - Thermal-Structural physics(via Joule Thomson effect & Thermal stress/strain). Please provide any good source of mathematical relations describing the above complete or in part...

Homework Statement Consider a parallel universe where the laws of nature as we know them are different, and aqueous solutions can have an excess charge. Two beakers are separated 1.20 meters and each contains 0.300 L of an aqueous solution of 6.40 × 10-6 M excess charge. One beaker has a net...

Greetings historians of physics! Newton's Principia is written almost entirely using geometrical proofs and diagrams, barely using any calculus at all. It is thought that Newton was reluctant to use his calculus in this work, fearing that it would undermine its credibility and reception, since...

I'm really stressed out at where I should be in my college career. In high school, I had taken trigonometry and analytical geometry. But when I went to college and took calculus, I was completely dumbfounded on what was being taught. I felt like I should have known the material. Google tells me...

Homework Statement dx(t)/dt = N0*sin(omega*t) * x(t) - ( N0*x^2 / k ) Omega,N0 and k are positive . Homework EquationsThe Attempt at a Solution I tried to solve it using the Bernoulli equations but I could not get the last result.

can someone suggest a method to solve an integral of the form analytically? ##\int \left[\frac{1}{(1+x^{2})}\right]^{-n}e^{-x^{2}}dx##

How to derive the formula to find the bending stiffness of an isotropic tapered tube which is cantilevered with a point load applied at the free end?

Can you prove a differential equation has no analytical solution? Teach me ,please! Thank you a lot!

Hello everyone. I'm taking two physics courses this semester. Analytical Mechanics and Waves. I was hoping if you guys could help me out a little and recommend some good books for both courses. Also, if you know good lectures that were recorded and I have access too (YouTube for example) I...

What is a reasonable analytical writing GRE score for a science/math/engineering programs? I had something like a 4.5/6.0 which seems kind of mediocre. I talked to some professors about why the general GRE is required, but they said that it was mainly aimed towards testing international...

Hi there I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as: E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2 If solved properly, it should give one curve (RHS), crossed...

Homework Statement Solve for X in the DARE (Discrete-time Algebraic Riccati Equation) analytically. A is diagonal A = [-a\;0; 0 \;a], and B = [b; 0] (in MATLAB notation). Any help is very much appreciated! Homework Equations The DARE is given as A'XA - X - (A'PB+S)(B'XB+R)^{-1}(A'XB+S)' + Q =...

Homework Statement I am calculating matching impedances for a source and its load using 2 different L-network topologies. One is: source-parallel-to-C, load-series-to-L and the other is: source-parallel-to-L, load-series-to-C. I go through all the calculations and notice that...

Hi all, I in my text they first did a phasor-diagram solution to a series LCR circuit and brought Z= under root of (R^2 +(Xc^2-XL^2)). After this they use a differential equation for series LCR circuit and actually did not solve such hard two degree differential equation, rather they...

Homework Statement A point particle of mass m is confined to the frictionless surface of a spherical bowl. There are 2 degrees of freedom. 1. Prove that the equilibrium point is the bottom of the bowl. , 2.Does the bowl need to be exactly spherical for this to be true ? 3. Near the...

Is there any analytical way to prove that the integral \int_{2.04}^\infty \frac{\sin x}{x^2}dx is nonegative? I tryed to use geometrical approach, i.e. the graph of the integrand look like: The magnitude became smaller and smaller, since \sin x is multiplied by the decreasing function...

Homework Statement I'm following a procedure in a particular paper as part of my Masters project. The paper is called 'Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials - Y Zhang, J Wen, Y Xiao, X Wen and J Wang (2012)' and can be seen...

As the spring semester is over and the summer is now beginning I was thinking that I would like to get a start on analytical mechanics on my own as a summer project. I was wondering if anyone knows an online lecture series on analytical mechanics, preferably with an assigned textbook and...

hey pf! i was wondering if you could help me out with a pde, namely $$\alpha ( \frac{z}{r} \frac{\partial f}{\partial r} + \frac{\partial f}{\partial z} ) = \frac{2}{r} \frac{\partial f}{\partial r} + \frac{\partial^2 f}{\partial r^2} + \frac{\partial^2 f}{\partial z^2} + 2 \frac{z}{r}...

I am going to quote an article below and there is a part I would like clarification.I do not understand why chaotic differential systems do not have an analytical solutions. In the simplest form,an equation such as this one [sin(x) + x - 0.5 = 0] does not have an analytical solution i.e it can...

Hello everyone, I have the following coupled ODEs ($$r\geq 0$$) $$g^2v^2f(r)h^2(r)+\frac{6}{r}f'(r)-3f''(r)=0$$, $$r^2h''(r)-4f^2(r)h(r)=0$$, with boundary conditions $$f(\infty)=1$$, $$h(\infty)=1$$. The other 2 boundary conditions are arbitrary. Also v and g are constants, that could be...

Homework Statement This is a mechanism I'm working with for my undergrad project (its Modelled in Msc ADAMS) https://www.flickr.com/photos/35430110@N04/13902494524/ https://www.flickr.com/photos/35430110@N04/13902494524/ And to give you an idea of how it operates; position 1...

Vector algebra and analytical geometry textbook I have a very comprehensive textbook written in portuguese about vector algebra and analytical geometry, but the author didn't include a bibliography at the book's end. What textbooks, in english, contains these syllabus (I'm pasting the list of...

Hi, Homework Statement I was given the setup in the attachment and was asked to find the angular frequency of small oscillations around the equilibrium. m1=m; m2=√3m Homework Equations The Attempt at a Solution I have found L = 1/2*(3+√3)*mR2\dot{θ}2 + mgRcosθ+√3mgRsinθ and the...

If a polynomial equation is solved for multiple roots in a system of equilibria (e.g. calculating extent of a reaction, or solving for [H+] in a complicated acid-base system, to give two basic examples) how do we know which, among the roots, is the correct solution (e.g. the correct extent or...

Dear All, I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution. \frac{dx}{dt} = 2Wx + 2xy - 4x^{3}\frac{dy}{dt} = \gamma \, (x^{2} -...

I haven't seen it asked on this forum before, so here goes: I am coming up on a third official attempt on the general (computer based) GRE soon. In my first two attempts I have not been able to break 50th percentile on the quant section, which is embarrassing. I have discovered that I do much...

Homework Statement Calculate the pH of 5.0 x 10^-8 M HCLO4. What fraction of the total H+ in this solution is derived from dissociation of water? Homework Equations The Attempt at a Solution The only thing I know to do is take -log(5.0 x 10^-8) .