Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

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can someone please explain how to get the The coupled first-order Dirac equations and the upper and lower spinor

$$ \begin{array}{l} \left(\frac{\mathrm{d}}{\mathrm{d} r}+\frac{k}{r}\right) F_{n k}(r)=\left[M+E_{n k}-\Delta(r)\right] G_{n k}(r), ..................(1) \\ \left(\frac{\mathrm{d}}{\mathrm{d} r}-\...
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how to find argument of $\sin(\sqrt{(\frac{k}{m})}*t+\phi)$ in a physics question about a spring?

[I think this question is more related to math than physics, so I've thought this forum is more approriate for the following question, let me know if it's not the case] I have this equation (it's the ...
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Integrating scalar field on a curve that is a line

As we already know (Theory): $$\int_c F(r(t))dt = \int_{t_0}^{t_1}F(r(t))\cdot|\frac{d r(t)}{dt}| dt$$ My example: We have a line $c$. And we have a constant $F$. However here since $F$ is a constant, ...
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Magnitude of torque due to weight in a simple pendulum

Suppose we have a simple pendulum as shown in figure . In this frame, suppose we fix $\theta$ as positive if rotation is at right of axis of symmetry (as depicted in figure) and negative if rotation ...
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How to obtain the period of this nonlinear differential equation?

Lately, I've been trying to find the period of an angle included in the following differential equations, but only could with the basic model: Basic or original: $$\mathrm{For}\ (\Phi (0), \Omega (0))=...
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Correct Setup of Coupled and Hierarchical Harmonic Oscillators

I am interested into understanding the behaviors of weakly coupled ascillators. Several books I have looked into give some really good insights and I wanted to look into a specific idea I had a bit ...
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Determining functional form of depth-dependent index of refraction, given transit time as a function of depth

A pair of radio receivers at known, fixed locations are placed atop a medium whose index of refraction varies as a function of depth. We may assume that this index of refraction has a known functional ...
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Need help in quantitatively modeling solubility of carbon dioxide in beer.

I'm trying to model a 3D surface which reflects the solubility of $CO_2$ in beer. An empirically derived chart is available at this link. Solubility is empirically related to the pressure of $CO_2$ in ...
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Deriving from Doppler's formula

I am studying Doppler sonography. I do understand doppler's formula: $$ f=f_{0}\frac{v}{v-u}, $$ where $f_{0}$ is emitted frequency, f is received frequency, v is speed of the ultrasound puls and u is ...
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How to solve this question? I tried changing velocity to m/s and also tried changing acceleration to km/h^2 but i cannot get the answer still.

A car is travelling at a velocity of $60km/h$. It then accelerates at $200m/s^2 $ for $2$ min. Calculate its final velocity? (Answer: 84km/h)
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Evaluate $\int_{-\infty}^\infty \frac{1}{(x^2 + D^2)^2}dx$.

$$\int_{-\infty}^\infty \frac{1}{(x^2 + D^2)^2}dx$$ Edit : $D> 0$. My work: Let $x = D\tan \theta$ $$\int_{-\infty}^\infty \frac{1}{(x^2 + D^2)^2}dx=\int_{-\infty}^\infty \frac{1}{(D^2\sec^2 \theta)...
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How to calculate the statistical uncertainty in a particle physics simulation?

I have a Monte Carlo code which simulates ions in a Tokamak. Most of the particles remain trapped forever. However, some of the particles escape. I can use my code to predict the fraction of particles ...
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What can't I transform physics question into math question properly? I try to find Brachistochrone curve, why do I find contradiction in acceleration?

I tried to find Brachistochrone curve myself, so I tried to set up equations about the $x$ direction and $y$ direction acceleration for the ball on the curve, and found something weird and probably ...
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Two blocks start from rest. Find acceleration of each block and tension in each cord.

The two blocks shown start from rest. The horizontal plane and the pulley are frictionless, and the pulley is assumed to be of negligible mass. Determine the acceleration of each block and the tension ...
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Eigenfunction expansion of a heat equation with Legendre polynomials

I am trying to solve the following PDE by performing an eigenfunction expansion: $$ \frac{\partial p}{\partial t} = -\cos \varphi \frac{\partial p}{\partial x} + D\frac{\partial^2 p}{\partial \varphi^...
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Cosine Integral (Lattice-discretized Laplace Equation in 2d)

$\newcommand{\rr}{\mathbf{r}}\newcommand{\ee}{\mathbf{e}}\newcommand{\qq}{\mathbf{q}}$ Hello community, I have been working on a sum for a bit. The idea is to derive a fundamental solution (Green's ...
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Oblique collisions question, how can coefficient of restitution be negative?

question: https://imgur.com/EfH4p8J, solution: https://imgur.com/PdZKk8A [2] As you collide with the wall, you will have a velocity before and after. So a formula the answer uses, where e is the ...
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How to calculate spectrum of a $3$-dimensional scalar field? [closed]

I have a data of three-dimensional turbulent scalar field $s(x,y,z)$ with $(x,y,z)\in [-3,3]\times [-3,3]\times [-6,6]$. The values of the scalar field are known and distributed on the regular grid ...
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Show exterior derivative is equal to this wedge product: $d F_5 = H_3\wedge F_3$

I have to show $d F_5 = H_3\wedge F_3$. This is one of the Bianchi identities for a solution of type IIB supergravity equation of motion, though I think that my problems are more mathematical than ...
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Uniform Horizontal circular motion of a car on a banked slope with friction.

I came up with this question, to try to help my understanding with uniform circular motion of an object on a banked slope: A car moving with speed $144$kmh$^{-1}$ is on a banked inward slope, the ...
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Can a 4D spacecraft, with just a single rigid thruster, achieve any rotational velocity?

It seems preposterous at first glance. I just want to be sure. Even in 3D the behaviour of rotating objects can be surprising (see the Dzhanibekov effect); in 4D it could be more surprising. A 2D or ...
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the deviation of the string from the equilibrium state is given by the function

I tried laplace but didn´t work. i don´t know how to start it
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What are the conditions for two vectors to be equal?

I am going through a derivation of a physics theorem (particulars are not important). It involves a sphere centered at the origin. The observation is made that $\hat{n} = \hat{r}$ (unit normal to ...
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Period of Cartan 3-form

A Cartan 3-form in a Lie group $G$ is defined as: $$\omega = Tr(g^{-1}dg\wedge g^{-1}dg\wedge g^{-1}dg)$$ For $g$ being maps $g:B\longrightarrow G$, with $B$ a given manifold. The so-called periods of ...
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OCR Further maths A Level Mechanics Exercise 4B Q 9: Question on circular motion

Two particles $A$ and $B$ of mass $40$g and $30$g respectively are attached to opposite ends of a light inextensible string of length $30$cm. Particle $A$ rests on a rough horizontal spinning table ...
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Dealing with second derivatives in error calculation

I need to find the relative error in the error of $\log P$, i.e. $\frac{\Delta(\Delta \log P)}{(\Delta \log P)}$. I need to prove that this equals $2\frac{\Delta P}{P\log P}$. I have tried so many ...
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Finding Acceleration of gravity and radius of a planet through a pendulum

A simple pendulum has a period of P on Earth. When taken to another planet of same mass, P decreases by 13%. What is the acceleration of gravity and the radius of the unknown planet?
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How to perform the following change of variables for a projectile with quadratic drag?

I have the following second order differential equation which explains the motion of a particle with quadratic drag to which I have done a reduction to a first order system. $$\frac{d}{dt}\pmatrix{x\\...
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Trying to model the Flyby anomaly

Thinking about it, the following non-linear ordinary differential equation crossed my mind: $$ \frac{d^2 r}{dt^2} - \frac{1}{2} H \frac{dr}{dt} + \frac{\mu}{r^2} = 0 $$ Apparently, I've been trying to ...
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Find at what initial velocity can the projectile reach $8534m?$ Find velocity and $x$ value when projectile reach $8543m$, without using Graph Method. [closed]

How can I solve this problem not graphically? If it is not possible, what more information do I need? At what initial velocity can the projectile reach $8534m?$ Find velocity and $x$ value when the ...
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Entropy increase in a finite set

A finite set M (playing the role of an energy shell $Γ_{mc}$) has $10^{100} − 1$ elements and is partitioned in $Γ_ν, ν = 1, . . . , 100$, with $\#Γ_ν = 0.9×10^ν$ . The “trajectory” (x(0), x(1), x(2), ...
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Question using cylindrical coordinates to find center of mass

I was just wondering if someone could please help me check my work/answer for this problem: Let $W$ be the ice cream cone region bounded above by the hemisphere $z=\sqrt{2-x^2-y^2}$ and below by the ...
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3 votes
2 answers
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Solution to $\int^{\infty}_0 \frac{1}{q} e^{-aq^2} dq.$

My apologies if this question has already been asked. I've tried using the search function but could not find the answer. I'm looking to solve the following integral: $$ \int^\infty_0 \frac{1}{q} e^{-...
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Position compensation after rotation

I am working in a game. I have a spaceship which can accelerate in any direction and can rotate around any axis (in 3D space). I want to have all other bodies in the world remain in exactly the same ...
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How to represent this one-dimentional movement in math?

I'm struggling trying to convert this movement behavior into an equation. For future reference, this is as a result of searching for a solution for a previous question of mine. Thank you @eyeballfrog ...
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Why this common eigenvectors do not depend on r?

I have the two following operators: $$ L_z=-i\hbar\frac{\partial}{\partial\phi} \\ L^2=-\hbar^2 \left(\frac{1}{\sin\theta}\frac{\partial}{\partial\theta}\sin\theta\frac{\partial}{\partial\theta} +\...
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2D Random Walk or just simple math?

I'm looking into a physical problem that involves the following sum: $$r(t)=\sum_{\substack{z_l=0,1\\1\leq l \leq N}}|b_{z_1z_2\dots z_N}|^2e^{-2i\epsilon_{z_1z_2\cdots z_N}t}$$ where $\epsilon_{...
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Rotating polar velocity vector fields

There is a great way to rotate a Cartesian vector field about the origin described in Rotating vector functions. Instead, let us suppose that we have a velocity vector field in polar coordinates i.e., ...
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What is the rms velocity of these 4 gas molecules?

Q) Velocity of 4 gas molecules are respectively 4m/s, 6m/s, 7m/s and 9m/s. What will be their rms velocity? (a) $\sqrt{45.5} ms^{-1}$ (b) $52m^2s^{-2}$ (c) $45.5ms^{-1}$ (d) $45.5m^2s^{-2}$ My attempt:...
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1 vote
1 answer
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Equivalence of reaction-diffusion

For $N$ cells in a one-dimensional ring, imagine a dynamical system given by, for each cell $1\leq i\leq N$ $$ \begin{align} \frac{dx_i}{dt}&=f(x_i,y_{i-1},y_{i+1})\\ \frac{dy_i}{dt}&=g(x_i,y_{...
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2 votes
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How do I calculate the gravitational force that a line-segment of uniform mass exerts on a point in 3D space?

For my purposes: The point can be assumed to always have a mass of 1. The mass of the line is uniform, and directly proportional to its length. Here is what I have so far: Let the line start at ...
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Constrained smooth transition between points.

Since I'm not very skilled at math, I'll try to explain my problem with apples. At a certain train station, every train driver has a specific route to cover everyday. A pair of brothers, who happen to ...
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2 votes
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Integrating a scalar with respect to a vector with vector limits?

The following is a line of reasoning you'll often see in physics textbooks. Newton's second law can be formulated in terms of momentum, which yields the following fundamental statement: $$\frac{d \vec{...
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1 vote
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Solving "when are these two exponential trajectories exactly distance ... apart"

I have two exponential functions related to a physics problem where two circles with same radius $r$ that are subject to non-linear drag travel with velocities $v_1=\{x_1,y_1\}$ and $v_2=\{x_2,y_2\}$, ...
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A Ray's Angle of Deviation for Double Rainbow

I'm attempting to find the angle that a ray of light comes out after going into a (perfectly spherical) raindrop traveling like this: See the attached diagram. The red lines are perpendicular to the ...
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How do I calculate the covarient derivative of a type (2,1) or (1,2) tensor

The following tensor I need help calculating the covarient derivative are as follows: and I know the general rule when it comes to a type (0,2) tensor is and I know the general rule when it comes ...
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1 vote
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Damped Natural Frequencies of a Multiple Degree of Freedom Mechanical System

I was wondering if there are any analytical methods to find damped natural frequencies of a general mechanical system that can be modeled with $$M\vec{\ddot{x}}+C\vec{\dot{x}}+K\vec{x}=0$$ where it is ...
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2 votes
1 answer
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Vector valued definite volume integral

In the context of a seminar lecture on some physico-chemical subject (magnetic shielding by electrons on atomic scale) I wanted to present a simple analytical example for the solution of an equation ...
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How can the oscillation of a dish be represented with an equation?

I am reading the book Surely You're Joking, Mr. Feynman! and I got to the point where he is eating lunch in the canteen when someone throws a dish and he thinks about the equation which represents its ...
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3 votes
1 answer
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Manipulation of delta (as in change) quantities

I am an undergrad physics student working through 4ed of Griffith's Electrodynamic book. This question is purely mathematical, however. Do not fret. In Griffith's (pg. 198), these equivalences are ...
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