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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1answer
38 views

The phase plane and potential energy

I think I have spotted a mistake in my notes, however I need help verifying my assumption: I am given the equation: $d^2s/dt^2=-s$ m=1 for simplicity I have recast it at a first order system: ...
0
votes
1answer
25 views

Finding units of measurement of coefficients in ODE's

If we have a question where we have to find the coefficient's units such as K in this case. The actual formula contains more parts but it is simply the derivatives that I am unsure about. ...
0
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2answers
35 views

A object was fired from ground with initial angle $\theta$

so i got that , a object was fired from ground with angule $ \theta $. when the object get the height equal to half of his max height , the velocity of object is $\frac{3}{4}$ of initial ...
0
votes
2answers
58 views

Time period for simple pendulum without trigonometry

The time period for simple pendulum formula that is $t = 2\pi \sqrt{\frac{l}{g}}$ is valid only for $15^\circ$ of amplitude. Why not more than that? How do I explain this someone who has just been ...
0
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1answer
24 views

Amount of Liquid in Container

Given: a cuboid container, of dimensions h into w into l a rate of flow of liquid per unit time through an inlet, in a rate of flow of liquid per unit time from an outlet, out, when the container ...
0
votes
1answer
53 views

Physics related Math Question about projectile motion.

Ok, if I am given an initial position (at the origin) and the final position coordinates $(x,y)$ as well as the initial velocity magnitude $V_0$. How do I find the correct initial angle that $V_0$ ...
4
votes
2answers
370 views

A relation between the law of multiplication with rate of travel and time.

I am reading the book Algebra for the practical man, chapter 1, article 6. Uptil article-6 the author has explained the operations of addition on positive and negative numbers. Now in article-6 he ...
1
vote
2answers
43 views

Calculate velocity after certain displacement

Given is a function $a(t)$ for the acceleration. Starting from an initial velocity $v_0$ I want to calculate the velocity $v_1$ after a certain displacement $s$. Is this calculation possible since ...
-2
votes
2answers
100 views

Studying maths for physicists [closed]

I am looking forward to be a theoretical physicist ,to unify general relativity and quantum mechanics ( to make the theory of everything ) How should I study maths? Should I study proofs of ...
1
vote
1answer
82 views

Energy Transfer in a Mechanical System - Standard Pulley Scenario

I understand that this is quite a basic question, I am new to dynamics and have trouble starting off questions, I found it quite difficult to find an example question alike to the one below thus I am ...
0
votes
2answers
47 views

Numerical Differentiation using Numerical Methods

I am currently studying Numerical Differentiation in MATLAB using Numerical Methods in Engineering with Matlab by Jaan Kiusalaas, and I am stuck at exercise 13 from Problem Set 5.1 from Chapter 5 ...
6
votes
2answers
142 views

Line Spectra in Hydrogen atom

Suppose you have a collection of large amount of Hydrogen atoms in $n$th state($n-1$th excited state). They have to go to their ground state($n$=1). Going from $n_1$ to $n_2$ makes a unique spectral ...
0
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1answer
65 views

PDE from London's Equation with Cylindrical Symmetry

The question is from ISSP by Kittel and as follows: (a)Find a solution of the London equation that has cylindrical symmetry and applies outside a line core. In cylindrical polar coordinates, we want ...
4
votes
2answers
112 views

Why do folded concentric circles and rectangles form a hyperbolic paraboloid?

Here is a "self-forming" origami that I made from folding concentric circles - it would also happen if I folded concentric rectangles. How can the fold shapes such a saddle-like geometry?
0
votes
1answer
45 views

Gauss' law of electrostatics

State Gauss' law of electrostatistics. A spherical charge distribution has a volume charge density given by $$\rho= \left\{ \begin{array}{lr} \rho_0\left(1-\frac{r^2}{a^2}\right) & ...
-1
votes
2answers
95 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
0
votes
0answers
11 views

looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
0
votes
3answers
41 views

Figuring out acceleration without knowing the time length

A car goes from 50mph to 20mph in an unknown amount of time. All that is known is that one of the car's wheels rotated 110 times during the process and that the wheel rotates at a rate that is uniform ...
2
votes
0answers
67 views

What if segments are not infinitely divisible?

I almost got myself mixed up I a philosophical discussion again. Somebody was talking about the Planck time and length which are, according to him, the minimal possible time and distance, and how ...
1
vote
0answers
40 views

Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
1
vote
0answers
16 views

How to calculate direction of ball upon collision?

I'm creating a game (Breakout) that involves a paddle and ball. I'm having trouble calculating the direction that I should send the ball after collision with the paddle. Currently, upon collision ...
1
vote
0answers
49 views

Approximate an integral

In a physics textbook, I came across the integral $$I(r_1,r_0)=\int_{r_0}^{r_1}\frac{1}{1-2m/r}\left[1-\frac{r_0^2(1-2m/r)}{r^2(1-2m/r_0)}\right]^{-1/2}dr$$ The author said that the integrand can be ...
0
votes
0answers
10 views

Finding the gravitational potential of a tilted disc?

Referring to this question: http://physics.stackexchange.com/questions/62637/the-potential-and-the-intensity-of-the-gravitational-field-in-the-axis-of-a-circ Suppose the disc was tilted at a 30 ...
0
votes
2answers
29 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
1
vote
1answer
35 views

How to find the total distance traveled, given the position function?

A particle moves in a straight line according to the rule $x(t)=t^3-2t+5$, where $x(t)$ is given in meters and where $t$ is given in seconds. Determine the position, velocity, and acceleration of ...
1
vote
2answers
77 views

Solving a differential equation?

I'm trying to analyze the transient state of a RC circuit. My book gives me the following differential equation: $$\frac{d(v(t))}{dt} + av(t) = c$$ for some constants $a$ and $c$. The book thens ...
2
votes
1answer
45 views

A question about the Laws of Thermodynamics [closed]

Many popular and semi-popular books about cosmology have appeared during the last few years in which the ultimate fate of the Universe is conjectured. One such scenario stipulates that space will ...
1
vote
1answer
85 views

When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?

As a follow-up to this related question, I'd like to know under what circumstances, if any, $\Delta x$, $\delta x$ and $dx$ all mean the same thing, and under what circumstances they can all be said ...
1
vote
4answers
120 views

Second order differential equation for acceleration

Can you help me understand and solve this question: A bullet is fired vertically upwards with an initial velocity of $u$. Form a second order differential equation for acceleration and by ...
2
votes
0answers
49 views

Clarification on some notation and “assumptions” in page 143-144 of the book “Quantum Fields and Strings: A Course for Mathematicians, Volume 1”

I was trying to read the chapter $1$ (at page $143$) of this book Quantum Fields and Strings: A Course for Mathematicians, Volume 1 that is supposed to be an introduction to modern quantum field ...
2
votes
1answer
64 views

What's the proper interpretation of canceling infinitesimals?

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
1
vote
1answer
79 views

How can the tension force be computed to test if a shape is moving or not?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
4
votes
2answers
114 views

A problem about symplectic manifolds in Arnold's book

There is a problem in Arnold's Mathematical Methods of Classical Mechanics which says that: Show that the map $A: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n}$ sending $(p, q) \rightarrow (P(p,q), ...
0
votes
0answers
28 views

stroboscope effect

I have a disc with a line drawn on one of his radius that is turning with frequency $f$, and I want to sample the place of the line to find the frequency of the disc. So we know from the ...
0
votes
3answers
106 views

Britney Gallivan's paper folding formulas

According to a few YouTube videos and New Scientist, formulas exist (based on algebraic/mathematical premises, thereby making this a valid math question) to describe the limits of paper folding. The ...
1
vote
1answer
35 views

Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
4
votes
1answer
66 views

Interpretation of Riemann rearrangement theorem [closed]

There's a common thing that happens in mathematics, which is that all theorems are created equal, but some are more equal than others. Here are two examples of what I mean by that. (1) In Euclid, the ...
4
votes
2answers
125 views

What are integrating factors, really?

I can follow the rationale for integrating factors well enough, but they still feel like voodoo to me. Every single description of integrating factors I've seen (and I've seen quite a few, including ...
2
votes
1answer
48 views

Integration problem related to physics problem

I want to know how to solve this (acytually this is the flux on any non-adjacent side of a cube due to a charge q on the vertice of the cube, side length: l) $$a=\oint\vec{E}.\vec{dS}=\oint ...
2
votes
1answer
86 views

Calculating stiffness and dampening for an oscillation to settle at a given time

The Problem How can I calculate a stiffness (k) and dampening (b) coefficient for an under-damped oscillation such that the system settles by a given time (t)? The Environment Given the ...
3
votes
1answer
77 views

How to compute force on joints of a 3D structure of balls connected by rods?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
1
vote
0answers
42 views

Variable density in the equation of motion

At a fixed point in time, consider the equation of motion $$ \nabla \cdot \boldsymbol \sigma(u) + \boldsymbol f = \rho \ddot{\boldsymbol u} \quad \text{in $\Omega \subset \mathbb R^d$} $$ for a ...
2
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0answers
72 views

How to maximize speed of rest position approach of nonlinearly damped spring oscillator?

Inspired by comments to answer for this question: Suppose we have a system which is described by the equation $$\ddot x=-x+g(\dot x),$$ with initial conditions $x(0)=1$, $\dot x(0)=0$. If ...
3
votes
1answer
157 views

Verify that $\nabla(A\cdot B) = (B\cdot\nabla)A + (A\cdot\nabla)B + B\times(\nabla\times A) + A\times(\nabla\times B)$

I'm trying to verify the following identity $$\nabla(\textbf{A}\cdot\textbf{B}) = (\textbf{B}\cdot\nabla)\textbf{A} + (\textbf{A}\cdot\nabla)\textbf{B} + \textbf{B}\times(\nabla\times\textbf{A}) + ...
2
votes
1answer
44 views

How can I prove the tangential acceleration equation?

This is my assignment for this weekend. $$a=a_{TT}+a_{NN} = \frac{d^2 s}{dt^2}\vec{T} + \kappa \frac{ds}{dt} 2\vec{N}$$ Actually, I want to why $a_N=\kappa (ds/dt)$ hold Please help me.
0
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1answer
24 views

Oscillating Object - Homework [closed]

I am forced to post this question here as physics SE refuses homework questions even if tagged with their (severely misleading) 'homework' tag. See my question at: ...
4
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0answers
36 views

C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata*

Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121: Nova introducitur ...
0
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1answer
36 views

Explanation on equations please [closed]

I've got seemingly two different equations for velocity in orbit: $$v_1 = \sqrt{ \frac{2GM}{R}} $$ and $$v = \sqrt{ \frac{Gm_e}{R}}$$ What is the difference between these two? I'm quite sure that ...
0
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1answer
19 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
0
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1answer
44 views

Proving the moment of inertia formula for right cylinder

I have a question on whether I can do this with an integral: When I tried solving this, I got (1/2)(M^2)(R^2) instead of (1/2)MR^2 Problem: http://i.imgur.com/QDdEEse.jpg *Sorry for lack of TeX. ...