Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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Describe a sine wave of known frequency with only two points

This is my first post on math.stackexchange (sorry if meta people remove the Hello (sometimes we do that over on stackoverflow ;P)! I have a system wherein I know that the output is a sine wave, with ...
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2answers
101 views

Work done by a force Field

Homework for Calc III includes a problem about computing the work done by a force field (defined by a specific vector equation) on a moving particle. I was attempting to compute this using the ...
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1answer
232 views

Trouble understanding a common vector calculus example

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
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3answers
191 views

Reflecting a golfball off a wall to a hole and compensating for the balls radius

Problem: I'm struggling to compensate for the radius of a ball when reflecting it off a wall towards a target. (sorry I cannot yet post images) What I want is to do this: golf reflections but this ...
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1answer
74 views

Solving a simple equation

I am just starting to study physics and I found this equation: $$\ x = 8 - {6t} + t^2$$ If possible please explain in a step by step. Sorry if it's too simple.
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1answer
123 views

Minimum Ejection Velocity

PROBLEM: Calculate the minimum ejection velocity with which a shell must be fired to strike a target 1000ft high and directly overhead. QUESTIONS: I use integration to work back from 32ft/sec and ...
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2answers
458 views

Up and Down Motion (Two objects meeting in time?)

PROBLEM: Suppose than an object is thrown upward with an initial velocity of 200ft/sec and that another one is thrown upward 5 seconds later with an initial velocity of 300ft/sec. When and where do ...
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1answer
400 views

Self-learning; Physics and Mathematics

My fields of interest are Physics and Mathematics. Gerard t'Hooft, 1999 Physics Noble Prize Laureate, has suggested a better scheme to study physics online. I can't wait for the university, so I've ...
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142 views

Where do I go from Linear algebra past Calc III to try to learn complex physics (relativity and quantum group theory)?

I'm mainly a programmer, but I have a love for Mathematics that's been, well, insatiable. I've had my eye on learning Quantum Groups and Relativity, but I want to stay in something I can do with ...
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1answer
192 views

Can rainbows be considered to have mathematical patterns?

Of course it is evident that there is physics and mathematics involved in a rainbow, but my question is (as the title suggests) are there patterns to be found in rainbows? By patterns I mean ...
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1answer
282 views

Moment of inertia of a circle

A wire has the shape of the circle $x^2+y^2=a^2$. Determine the moment of inertia about a diameter if the density at $(x,y)$ is $|x|+|y|$ Thank you
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158 views

Degree of maps on the 3-sphere

I am currently in the process of going through Ticciati's Quantum Field Theory for Mathematicians, which states the following (Theorem 13.7.11): "Let $g$ be a differentiable function from $S^3$ to a [...
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2answers
1k views

Resonance Frequencies of Oscillator

I understand that resonance is when the force term increases the natural oscillation of the system. In the next equation the oscillator has a natural frequency $\omega_0=\sqrt{\frac{k}{m}}$. But I don'...
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1answer
1k views

Coordinate Transformation on Local coordinate system

I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
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1answer
297 views

Geometry brain teaser (Candle in the room with mirrored walls)

King wants 2D room with smooth walls and columns (second derivative exists) that reflects light. King asks you to build it in such way that there exists a spot, where you can place a candle and there ...
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1answer
290 views

Electrostatic Potential Energy

How is the boxed step , physically as well as mathematically justified and correct ? Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy As work done = $- \Delta U $. for Conservative ...
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1answer
553 views

Find the time at which a particle projected up an inclined plane, comes to rest?

A particle of mass $m$ is projected up a plane that is inclined at an angle $\alpha$ to the horizontal. At $t=0$, its velocity is $v_0$ and the coefficient of dynamic friction of the slope is $\mu$...
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1answer
214 views

Difficulty in obtaining the Lorentzian lineshape for natural broadening

Not sure if this maybe belongs more in the maths section, but since it comes from a physics problem i'll post here. when calculating the natural broadening lineshape for a laser we have to take the ...
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0answers
40 views

Velocity and Distance; Functions of Time

$s(t)$ = distance a particle travels from time $0$ to $t$. If in this case, the distance $s$ is only the function of time then its necessary that the velocity should be constant. Likewise, $v(t)$ = ...
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2answers
60 views

Distance of a particle; a function its time

Force is a function of mass and acceleration. Here mass is a fundamental quantity, and acceleration is a derived quantity OR $F(a, m) = ma$. I want to ask that why the distance traveled by a ...
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6answers
1k views

What is this physicist saying?

I do not want to poison this forum with politics. But I want to understand, precisely, what is meant by the bolded statement. It is made by a physicist who used to work at Harvard regarding the ...
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1answer
408 views

Let $F(x,y,z) = -c(r/||r||^3)$ be the force resulting from the inverse square law…

$c$ is a constant and $r = (x,y,z)$. Show that $\displaystyle f(x,y,z) = \frac{c}{\sqrt{x^2+y^2+z^2}}$ is a potential function for $F$. What can be concluded from any path from point $A$ to point $B$ ...
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1answer
487 views

Calculating the angular velocity

I have an inverted pendulum with a accelerometer mounted on the top that at rest gives me a vector up opposite to gravity, which is used to calculate the angle of the pendulum. Is it possible to ...
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1answer
1k views

Derivative of a bra?

I understand that $$ \frac{\mathrm d}{\mathrm dt} \langle\psi|\psi\rangle =\left[\frac{\mathrm d}{\mathrm dt} \langle\psi|\right]|\psi\rangle + \langle\psi|\left[\frac{\mathrm d}{\mathrm dt}|\psi\...
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1answer
315 views

Integral - Problem

Hi I am stuck with an integral problem trying to show $$ -\int \frac{d^{3}p}{(2\pi)^3}p\frac{\partial f(p,t)}{\partial p}=3F$$ where $F=\frac{1}{(2\pi)^3}\int d^{3}pf(p,t)$ I have read in many books ...
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1answer
175 views

Nonlinear Second-order ODE BVP with 4 boundary conditions

My Lagrangian comes out in this form when I impose spherical symmetry: $$ φ''(ρ)+{3\overρ} φ'(ρ)+{4μ^4\over M^2} φ(ρ)-{4μ^4\over M^4} φ^{3}(ρ)-{μ^4\over2M} ϵ=0 $$ The following boundary conditions ...
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1answer
44 views

Are there solutions when the boundary conditions are particle positions at 2 different times instead of positions and speeds at an initial time?

Is it possible to find solutions for a dynamic system when the boundary conditions are particle positions at 2 different times instead of positions and speeds at an initial time? The question is ...
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2answers
356 views

Generally covariant Klein-Gordon equation

Consider a 4-dimensional smooth manifold $M$ on which there is a Lorentzian metric $g_{ab}$ and a function $\phi$ satisfying the following two equations (in abstract index notation): \begin{equation} ...
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0answers
103 views

Using the integral equation, find the eigenvalues and eigenfucntions

The integral equation: $$ \int_{-\frac{T}{2}}^{\frac{T}{2}}dt' \phi (t')e^{\Gamma\left | t-t' \right |} =\lambda \phi(t) $$ for $(-\frac{1}{2}T< t < \frac{1}{2}T)$ is useful in photon ...
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1answer
516 views

Consider a pendulum that that has a length of $50$cm …

I am trying to do a simple pendulum problem but for some reason my answer is different from the book's answer and I don't know what I am doing incorrectly. The question is: Consider a simple ...
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1answer
50 views

Is this a set of generators for the conformal group of Minkowski space?

My physics textbook asserts that the group of maps $f: M \rightarrow M $ ($M$ is the Minkowski space, i. e. $\Bbb R^4$ with the pseudonorm $||x||=x_0^2-x_1^2-x_2^2-x_3^2$ and scalar product $x\dot{} ...
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69 views

Units in this problem: velocity or distance?

I know this is slightly off-topic here, but it's really bothering me. My class was given the following immensely simple problem today: A bird flies due south at a constant speed of $45\frac{\text{...
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254 views

Give a physical explanation for why the Neumann Problem has no solution?

Give a physical explanation for why the Neumann Problem $$ U_{xx}+U_{yy}=q(x,y) $$ $$ \nabla U(p)\cdot n(p)=g(p) \quad \forall p\in C $$ on $D$ for Poissons equation, has no solution, unless we ...
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Is it better to learn math before physics? [closed]

It seems that a persons ability to understand physics at a high level is limited primarily by their understanding of math. It also seems to be more efficient to learn the underlying math for a ...
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1answer
152 views

Find all solutions of the 1-D heat equation of a specific form

I'd like to find all solutions of $u_t$ = $u_{xx}$ of the form $$u = \left(\frac{1}{\sqrt{t}}\right)v\left(\frac{x}{2\sqrt{t}}\right).$$ I know that this problem reduces to solving a second order ...
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1answer
270 views

Bullseye-shaped interference pattern in seminar-room chair

During a break n a seminar today, I noticed that the chairs in front of me all had slightly transparent black mesh fabric. The backs of the chairs were in the shape of a hyperbolic paraboloid. The ...
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510 views

Diadics and tensors. The motivation for diadics. Nonionic form. Reddy's “Continuum Mechanics.”

I'm taking a course in continuum mechanics. Our book is Continuum Mechanics by Reddy, a Cambridge edition. In the second chapter he introduces tensors and defines them to be polyadics. He is ...
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1answer
50 views

Observer in magnetic and electric fields

respect an inertial observer O, I have an object of weight m and charge $q$. It is in a electric field $E=(E,0,0)$ constant and a magnetic field $B=(0,0,B)$ constant. I have another observer o' that ...
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1answer
3k views

How is the formula for the focal point of a ball lens derived?

How can the focal point of a ball lens be found?
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731 views

How to calculate work

What is the work done by the force of gravity on a particle of mass $m$ as it moves radially from $7500 ~\text{km}$ to $9400 ~\text{km}$ from the center of the earth?
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566 views

Solve a differential equation using Fourier series

Assume I have a second order differential equation $\ddot{x} = F(x,\dot{x})$ (or an equivalent equation of first order) and that I know there is a periodic solution to it (for simplicity's sake, ...
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59 views

Taylor expansion of an integral in spherical co-ordinates

I've some difficulty deriving this equation from jackson electrodynamics (The equation after 1.30) $\nabla^2 \Phi_a\left({\textbf{x}}\right)=-\frac{1}{\epsilon_0}\int_{0}^{R} \frac{3a^2}{\left(r^2+a^...
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1answer
373 views

Uncertainty in Acceleration given the uncertainty in position

I had a motion detector record the position of a dynamics cart and automatically plot Position vs Time and Velocity vs Time plots in Logger Pro on the computer. If the instrument uncertainty in ...
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2answers
442 views

Matrices/physics

Hello everyone, I'm stuck on this question and help would be very much appreciated. I get particularly confused with the sign conventions when applying KCL and KVL. Somehow I have to incorporate ...
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2answers
383 views

Vector Components - Superposition of Forces

I understand that by inspection of the given figure, $F_{1,x}$ (the x-component of $F_1$) must $< 0$, so $F_{1,x} = 250\color{red}{\cos{53^{\circ} }}$ can't be right. But I don't see how $F_{1,x} = ...
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1answer
402 views

Complex parametrization of Airplane wing?

I read once about complex parametrization with fluid-dynamics objects such as airplane wings, something related Rieman Zeta function. What are the mathematical models this kind of things such as ...
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41 views

Three body problem with point interactions

I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials). Is ...
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3answers
594 views

Is this an undergraduate-level proof of conservation of energy, or an arbitrary manipulation of symbols that happens to give the right answer?

This is a slightly farcical question, for which I apologise. An undergraduate tutee of mine was faced with the following problem: Q. A particle of mass $m$ moving along a line is subject to a force $...
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1answer
442 views

Determine the Fourier Transform and Fourier Series of the function

$$ f(t)=\frac{\sin(at)}{t} $$ Since the term is parameterized, it's easy to see that if I take the first derivative with respect to 'a', then the function becomes considerably easier. I do this to ...
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1answer
2k views

Using a Fourier Transform and Parseval's Theorem to Solve an Equation

I'm sorry to bother you, but I've been studying for a test, and I kinda got stuck in this question. Let me place the question then tell you what I've done so far. I have to find the Fourier Transform ...