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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Metric Multidimensional Scaling for Geometric TDoA Array Calibration

Background I'm following this paper, and this Matlab code by the author (see Slide 4), in an attempt to implement metric multidimensional scaling for the calibration of geometric Time-Delay-of-Arrival ...
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How To Use A Line Integral To Calculate The Work Done By An Object Falling Down A Parameterised Curve?

I am trying to calculate the work done by a unit mass which falls along a parabola from (5,25) to (0,0) (where the gradient at (0,0) is 0). My solution was to use a line integral. I parameterised the ...
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Solving $\ddot r=-\frac{GM}{r^2}$ [closed]

In finding a comet's equation of motion, I derived this: $$\ddot r=-\frac{GM}{r^2}$$ I have never encountered ODE like this before this time. How do I solve $r$ with respect to time, $t$?
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Gravitational geons: an explanation for mathematicians

The Notices of the AMS has a column that is What is...?, I would like to ask in the spirit of this journal about a subject in which I'm interested. I wondered if some user can to expand the ...
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Simple conservation of momentum question...am I right?

I was doing a very old Applied Mathematics exam (from the 70s... yeah I lead a sad life) and came across the following problem. A shell is fired from a gun mounted on a carriage which is moving ...
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A very hard gaussian integral

There is an integral I read in a book that I don't understand. First I have equation $(4.56)$ like this: \begin{align*}& \exp(-\frac{1}{2}\sum_{j=1}^{n_2}\sum_{\alpha_1,\alpha_2\in D} \hat{G}^{\...
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-1 votes
2 answers
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How much of the earth can see the moon? [closed]

I framed this into 2d. If you draw two circles, get the common direct tangents, then you need to find the angle between the two intersection points for the two lines and the bigger circle. Except I ...
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Prove when Instaneous Velocity is equal to Average Velocity with Constant Acceleration

Assume constant acceleration. It seems that average velocity over some time interval [t1, t2], will be equal to the instantaneous velocity at the midpoint t = 1/2[t1 + t2]. I'm wondering how you might ...
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Find the velocities after impact and the loss of kinetic energy. [closed]

A sphere of mass 3 lbs., moving with a velocity of 7 ft./sec., impin ges directly on another sphere, of mass 5 ha.. at rest after the impact, the velo cities of the spheres are in the ratio of 2:3. ...
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1 answer
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Find a formula/function based on dataset

I have an example dataset with each row having two variables. The shown data uses Time and Distance Time Distance 0.2388839976 212.54885537138 0.3349551193 337.83087805091 0.3703744125 398....
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Understanding complex exponentials as solutions to differential equations

I am a physics undergraduate working through of Jackson E&M (3ed)'s section on solving Laplace's equation in cylindrical coordinates. I am consciously asking this question on Math stack. I have ...
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Diffraction Intensity = Fourier Transform of the Autocorrelation

I'm trying to understand how x-ray diffraction intensity is related to the Fourier Transform autocorrelation function. In the work below, $\rho(\mathbf{r})$ is the electron density of a molecule/...
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2 answers
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How can I solve a differential equation of the form $c_1 \ddot{x}^2 + c_2 \ddot{x} + c_3 \dot{x}^2-c_4 =0$?

The solution to it will give us the eqs. of motion of a car moved by a constant force due to combustion of fuel at the engine that produces the main torque at the wheels and that is "fighting&...
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1 answer
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Mechanics of a weighted rod held at one and

We need to show that the tension in the rope, T, is = to 2Mgcos(theta) I've taken Moments about A but keep getting T = (1/2)Mgcos(theta). I've ignored the moments at C as they are in equilibrium ...
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1 answer
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Work of weight force

I'm trying calculating the work of weight force of a punctiform mass, free falling from an height L . We know that total work along the path is given by dot product between force and displacement, ...
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1 answer
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Physical interpreation regarding heat equation

I have included image of a problem from Oxford. I was able to do the question. However, i am stuck at the last part which asks about the physical interpretation. I don't have a good background in ...
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1 answer
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A particle is executing oscillations about the origin on the X-axis. Its potential energy is $U(x)=k|x|^3$.Find ansatz of integral wrt parameter.

A particle of mass $m$ is executing oscillations about the origin on the X-axis. Its potential energy is $U(x)=k|x|^3$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then ...
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1 vote
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Systematic way of solving this charge-placement problem without brute force

This is a problem I encountered on an exam. I understand the problem and what needs to be done but I cannot figure out a way to solve it systematically other than brute forcing. It deals with physics ...
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1 vote
1 answer
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Full derivation of impulse formula for collision response

The wikipedia page says that the equation for impulse-based collision response is: \begin{equation} j_r = \frac{ -(1 + e) v_r \cdot n } { {m_1}^{-1} + {m_2}^{-1} + ({I_1}^{-1}(r_1 \times n) \times ...
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1 vote
1 answer
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the centroid of a plane area - how to interpret 1/2 in the summation formula for Mx?

Please explain why "1/2" appears in the following summation. My understanding is that Mx = y*(dA), so I'm looking for an interpretation of the 1/2 factor there especially, as for y=f(x) and ...
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1 vote
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Two operators multiplication in the Baker-Campbell-Hausdorff Lemma

When I was learning the transformation from the Schrodinger picture to the interaction picture in quantum mechanics, I have to use the Baker-Campbell-Hausdorf Lemma, \begin{align} e^ABe^{-A}=B+[A,B]+\...
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2 votes
1 answer
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Performing receiver localization in media with non-trivial refraction properties using TDoA

Problem. I have a radio transmitter, with known location $\langle t_x, t_y, t_z \rangle$, embedded in a medium whose index of refraction varies as a known function of depth: $$n(\text{depth}) = a-be^c$...
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Deriviation of terminal velocity with faulty results, under condition that $f=-cv^2$

Note: There's a similar problem to this (https://math.stackexchange.com/questions/2796694/how-to-derive-an-equation-for-terminal-velocity-assuming-air-resistance-is-some#:~:text=Taking%20proper%20sign%...
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How would we calculate the density of particles inside a 1 dimensional Universe?

How would we calculate the density of particles inside a 1 dimensional universe. The particles can only interact with each other through Newtonian gravity and will pass right through each other. the ...
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1 answer
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What mathematics books would be good to get an understanding of Lie Groups and how they relate to the symmetries of fundamental particles?

I have a math background and am familiar with multivariable calculus but seem to get lost when I read how it may be related to "gauge symmetries" of fundamental particles. The nuts and bolts ...
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additivity of elements in Baker–Campbell–Hausdorff formula

When I was learning the interaction picture of the Hamiltonian, the usual way to convert it from the Schrodinger picture is using the Baker–Campbell–Hausdorff formula, \begin{equation} e^ABe^{-A}=B+[A,...
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2 votes
2 answers
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Double delta function value

I have a question from a past paper of a university physics course. "Calculate $\int_{-\infty}^{\infty}\delta(y-x)\delta(y-z)dy$" We believe the answer is $1$ only if $x=z$, otherwise the ...
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-1 votes
1 answer
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Questions on direction of dot product

So i am having problems with understanding that if two forces (suppose in parallelogram law of addition of two vector) the resultant has the same direction as the diagonal between them. So theta (...
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0 answers
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Equation containing $\arcsin$ as well as square root.

I was studying physics for an upcoming exam and found this in a practice sheet : A source S is oscillating between A and C with its position varying with time as $\displaystyle y (\text{in metres})=...
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2 votes
2 answers
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Is curl of a particle's velocity zero?

The question Consider the motion of a particle specified by $\mathbf{x} (t): \mathbb{R} \mapsto \mathbb{R}^3$, where $\mathbf{x} = (x_1,x_2,x_3)$ in cartesian coordinates. The curl of its velocity $\...
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Bounce a vector off multiple hyperplanes

Given a unit vector $x\in\mathbb{R}^n$ identifying a hyperplane, it is possible to "bounce" another vector $v\in\mathbb{R}^n$ against this hyperplane as follows $$ v' = v - 2(v^\top x)x, $$ ...
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1 vote
1 answer
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Is there any mathematically rigorous way to represent the density of vectors in a vector field? [closed]

A vector field is a function which associates a vector to every point in $\mathbb{R}^3$. In other words, a vector field is a function which takes every vector in $\mathbb{R}^3$ as input and outputs ...
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Modified Bessel functions from Integrals

I have the following integral from a Physics paper (equation 40): \begin{align*} -\int_{0}^{\infty} dy_{\perp} \Bigg[\int_{-\infty}^{-l} dz_{\perp}\Bigg(\int_{-\infty}^{\infty} \frac{dk_{\perp}}{2\pi} ...
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4 answers
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Why the wire is represented by $y$? why $\bar{x} = 0$?

Here is the problem in Stewart "Calculus, early transcendentals, 9th edition" My question is: Why the wire is represented by $y$ in the equation that expresses the density? why $\bar{x} = 0$...
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2 points on a physical plane. Ideal path to connect them for maximum marble rolling speed? What kind of math is this?

Say there are 2 points on a physical plane. You can connect them in infinite paths. Line, parabola, S-curve, L-curve, etc. You roll a marble between the points on said constructed path. There ...
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3 votes
1 answer
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Equilibrium problem with 3 unknown forces | Hanging mass

This problem is related to my previous question on the generalized Lami's theorem. I would like to see how you solve this problem and compare with my solution. My motivation for this problem is that I ...
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0 votes
1 answer
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If E and H are divergence-free and the time derivative of each other, then why is the Laplacian just the second time derivative?

Suppose \begin{alignat*}{2} &\nabla\cdot E=0\quad\quad\quad&\nabla\cdot H=0 \\ &E=-\frac{\partial H}{\partial t}&H=-\frac{\partial E}{\partial t} \end{alignat*} I need to show that \...
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1 vote
1 answer
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How do I calculate the maximum speed reached by an object that moves a given distance with a given maximum acceleration and jerk?

I am exploring the math of simple linear motion. Consider an idealized object that starts stationary at the origin, moves to some displacement $d_{max}$ from the origin, and then stops. Additional ...
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5 votes
1 answer
332 views

Generalizing Lami's theorem

In statics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly ...
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0 votes
1 answer
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Is $\text{Tr}(U^{-1}) = \frac{1}{2} (\text{Tr}(U) ^2 - \text{Tr}(U^2))$ for $U \in SU(3) $? [closed]

Is it true that $\text{Tr}(U^\dagger) = \frac{1}{2} (\text{Tr}(U) ^2 - \text{Tr}(U^2))$ for $U \in SU(3) $ ? In particular are there more general formulas/ systematic way of reducing higher powers of ...
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11 votes
0 answers
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Is there a simple maximally general generalization of Noether's theorem to arbitrary dynamical systems?

Noether's theorem informally states something like "symmetries in the dynamical law imply conserved quantities". However, the theorem is generally stated in terms of physics-specific classes ...
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1 vote
1 answer
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Question about Intermediate Value Theorem and phrasing proof

During a move, Driver A and Driver B drove two separate cars from their home town, Washington D.C. to New York City. It took them about 5 hours to travel to NYC. They agreed to travel no faster than ...
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Confused about number precision

As far as I know, precision is defined as how close a number of result are. e.g. We don't say that 65 is more precise than 60. Instead we say that 50, 51 and 49 are more precise than 55, 65 and 40 ...
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2 votes
2 answers
77 views

Peskin and Schroeder, Eq 2.51 with a spacelike interval.

From the book "An Introduction to Quantum Field Theory" by Peskin and Schroeder, in page 27, they give the following derivation: We have the amplitude: $$ D(x - y) = \frac{1}{(2\pi)^3} \int \...
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1 vote
1 answer
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Damped oscillation in a path.

I saw this video, and in this minute, proposes the following equation: $$ y + k_1 \;y'(x) + k_2 \;y''(x) = f(x) + k_3 f'(x) $$ This is the equation that a "particle" would follow if attached ...
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$\cos\theta=\sin(\theta\pm\frac{\pi}{2})$?

This question came in the Dhaka University admission exam 2019-20 Q) Two particles are oscillating with simple harmonic motion. If their displacements are described by $x_1=A\sin\omega t$ and $x_2=A\...
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2 answers
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Deriving the equation of motion of an harmonic oscillator from the equation of motion of a mass-spring system

During my physics 1 course I stumbled upon this problem (our professor left it as an exercise). Basically I have to prove that $$A\cos(\omega t) + B\sin(\omega t) = C\cos(\omega t + \varphi )$$ and ...
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can someone please explain how to get the The coupled first-order Dirac equations and the upper and lower spinor [closed]

$$ \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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1 vote
0 answers
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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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0 votes
1 answer
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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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