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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2answers
48 views

What's a method for computing the indefinite integral $\int \dfrac{dz}{(a^2 + z^2)^{3/2}}$?

This integral occurs in EMFT when computing $\overline{E}$ due to an infinite line, uniform charge distribution. I'm trying to figure out the formula for $\int\dfrac{dz}{(a^2 + z^2)^{3/2}}$, using ...
1
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0answers
23 views

How to do this Poisson bracket proof

For the proof of the above equation, I understand the first step which has been obtained from the definition but in the second step I don't understand why they are summing over $j$ first ...
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1answer
19 views

Poisson bracket proof

For this question I understand the first line of the solution which they have obtained from the definition but how have they simplified each term to get to the second line from the first line? The ...
7
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1answer
100 views

Is the regularization of a Fourier transform unique?

The Fourier transform of the Coulomb potential $1/\vert \mathbf r \vert$ of an electric charge doesn't converge because one obtains $$F(k)=\frac {4\pi}{k} \int_0^\infty \sin(kr) dr.$$ The standard ...
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0answers
21 views

decreasing travel time over an arc

I am trying to write a program that travels along the same arc but each iteration the travel time needs to decrease. I have been trying to do this by changing the starting velocity and acceleration. ...
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0answers
21 views

Elliptical orbits and differential unit angle? What's $d\hat{\theta}/d\theta$

I was reading a short article on the derivation of the elliptical orbits of bodies under the influence of inverse-square gravity, and it goes something like this: $m\frac{d\vec{V}}{dt} = ...
1
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1answer
32 views

Poisson bracket proofs

I understand the first sentence you wrote for the need of a different summation index. However, i'm still not able to understand the individual steps. Like how in the first line we have four ...
0
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1answer
28 views

Justification of manipulations used to solve a physics problem.

Problem. A particle moves in a deaccelerated manner, describing a circular trajectory of radius $r$, having an initial speed $v_0$. Suppose $a_n=-a_t$ (normal acceleration and tangential ...
28
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5answers
863 views

Why does adding a term $5f'(t)$ to $5f''(t)+10f(t)=0$ cause damping?

So we have a differential equation to model an oscillator: $$5f''(t)+10f(t)=0$$ Where the initial conditions are $f(0)=0$ and $f'(0)=4$. It is given that $f(t) = \frac{2\sqrt 2}{5}\sin\sqrt2 t$. ...
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3answers
23 views

Basic problem on deceleration

A car accelerates from rest for $15$ s with a uniform acceleration of $1.5$ m/s^2 and immediately decelerates with a uniform deceleration of $5$ m/s^2. How long does deceleration take? I used ...
3
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1answer
35 views

Can we interchange derivatives when multiplied?

Although this looks like a physics question, this is more of a Math question, I was reading the Energy-Mass relationship derivation, it goes as follows, Force $F$ is given by ...
1
vote
1answer
49 views

Escape velocity

Calculate the escape velocity from a white dwarf and a neutron star. Assume that both the white dwarf and the neutron star is 1 solar mass. Let the white dwarf’s radius be $10^{4}$ kilometres and the ...
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0answers
20 views

What is the gravitational potential of an ellipsoid at $0$?

What is the gravitational potential of an ellipsoid at $0$? Given an ellipsoid: $\frac{x^2+y^2}{a^2} +\frac{z^2}{c^2} \leq 1,$ and a uniform density of mass: Using spherical coordinates, and the ...
1
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1answer
55 views

Simplifying a complex trigonometric expression

Context: In a previous question , I've stated I'm making a program that will be used for calculating stuff with Statics of a particle. I've come across another scenario in which there's three forces ...
0
votes
1answer
26 views

How to make vector from azimuth and speed?

I don't know how to make $3$D vector of speed from azimuth and speed. Azimuth is in degree and speed is in m/s. Azimuth is angle on $X$ and $Y$. Thank you for your help!
2
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2answers
37 views

Least squares regression with two predictor variables (exponential functions of time)

Question cropped from textbook (Apologies for the link- I don't have enough rep to post the actual image.) [Now pasted below. Ed.] I've come across a question in a textbook (linked above) requiring ...
3
votes
3answers
453 views

Find equation for mass in gravity

A satellite is moving in circular motion round a planet. From the physics we know that $$\Sigma F_r = ma_r = \frac{GMm}{r^2}$$ So I wanted to find the equation for $M$ knowing also that $$v = ...
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2answers
21 views

Normalizing the Simple (Quantum) Harmonic Oscillator for $n=2$

I am trying to find the constant for the second excited wave state that will normalize it. The equation for the second excited state is $$\psi_2(x)=A_2(1-\frac{2m\omega ...
2
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2answers
31 views

Find an function that oscillates between a given upper and lower envelope

Suppose I'm given two real, continuous functions $f(x)$ and $g(x)$ such that $f(x)\ge g(x)$ for all real $x$. I'd like to determine an oscillating function $h(x)$ that has $f(x)$ as its upper-envelope ...
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0answers
13 views

Simulation missiles - initialization vector

I'm trying to implement a simple simulation of the trajectory of bullets. Only for school project. I am using formula: ...
0
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1answer
17 views

How to calculate work done on standing a rod upright with arbitrary mass distribution m(x)

I was way overthinking how to calculate calories that you would do performing a pullup, which is a straightforward mgh. But with a sittup, you have some non-uniform torso that's being lifted to ...
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0answers
41 views

Hydrostatic force on a dam

A dam is inclined at an angle of 30° from the vertical and has the shape of an isosceles trapezoid 200 ft wide at the top and 100 ft wide at the bottom and with a slant height of 160 ft. Find the ...
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1answer
35 views

Rocket simulation. Are my equations correct?

I am simulating a rocket launch (two dimensions) and I am a little unsure about my implementation of Euler Forward. I will only give the $x$ component since $y$ is done the same way. I first ...
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3answers
67 views

Having trouble simultaneous trigonometric equations

I'm racking my brain trying to solve some formulae that I will need to implement into a program I'm making. The program is based around statics of a particle, as in that all forces acting on the ...
0
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0answers
19 views

Solving the finite square well graphically (Transcendental Equations)

I am attempting to comprehend how they are solving these transcendental equations here. The equations they derive are $\tan(ka)=\frac{\alpha}{k}$ which gives the even solutions and ...
0
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2answers
27 views

Find distance as function of time.

A car starts from rest and accelerates in $a = \frac{2\cdot m}{3\cdot s^3}t$, After $3$ seconds, The car will be $27$ metres from beginning. Find distance as function of time. I know i have to ...
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3answers
40 views

Free fall of 2 water drops

Cloud is showering 2 water drops from 1000 meters above the ground in 1 second difference. Let be Gravitational acceleration = $10\frac{m}{s^2}$, and Air resistance is negligible. What will be the ...
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0answers
13 views

Energy Conditions

Hi guys im trying to solve the energy conditions for a specific stress energy tensor but have come up at a stumbling block. How would i calculate the energy conditions for the following stress ...
0
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0answers
8 views

Entropy fix for 1-d conservation law with convex flux functions

Consider the following Riemann problem for a convex function $f$ \begin{eqnarray*} \partial _t q + \partial _x f(q) &=& 0 , \\ q(x,0) &=& q_0(x) =\left\{\begin{array}{ll} q_l ...
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0answers
33 views

Modelling diffusion in composite media (PDEs)

I have to construct and solve a system of PDEs for drug delivery through a transdermal patch. I have been given that the epidermis has thickness ${\delta}_1$ and coefficient of diffusion $D_1$, the ...
0
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0answers
8 views

Greens Function for poisson equation in cartesian along boundary

I am tryng to solve $$\nabla ^2 \phi = -\rho(\vec x)$$ Where $\phi(0) =0$ and $\phi(L)=\phi_0$ and $\rho$ is an arbitrary functionAccording to wolfram we can write G in terms of spherical harmonics, ...
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0answers
51 views

Angular moment (Hibbeler's book question)

This question's from the book HIBBELER, R. Engineering Mechanics: Statics; chapter 4. The curved rod lies in the x-y plane and has radius $3m$. If a force $F=80N$ acts at its end as shown, determine ...
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1answer
24 views

Einstein Summation Convention Minkowski Metric

Picked up a book on General Relativity for Mathematicians, but I'm a bit unclear on some of the tensor notation. For example, the Minkowski Metric $$\eta_{\mu \nu} (\Delta x^\mu)(\Delta x^\nu)$$ ...
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1answer
18 views

Showing that the integral of one equation yields another.

Background: The equations are derived from a Physics 2 Lab circuit that has a resistor and a capacitor Problem: Show that the integral of equation 5 yields equation 2. I'm given: ...
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3answers
31 views

Showing that one physics equation 'satisfies' another

Background: This is from a Physics 2 Lab. The equations come from a circuit that has a resistor and a capacitor I'm given these two equations $V - \frac{dq}{dt} R - \frac{q}{C} = 0$ <== ...
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1answer
48 views

Simulating a rocket in Matlab

I want to simulate a rocket. I found this code in a book. For the past two days I have been trying to understand it. For instance there is a line: ...
0
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0answers
30 views

Neumann condition and Dirichlet condition at the same point

I am studying heat equation on a 1-D bar. We now that Neumann conditions at both ends leads to a singular matrix (for finite element methods) in equilibrium. Adding an initial condition can lead to ...
2
votes
5answers
76 views

Let $\ddot x=2x$. If $\dot x$ is $0$ when $x=1$. Find $\dot x(x=3)$.

I was given this problem in a physics class, and below is the answer by the professor. ($x$ is position, $v=\dot x$ is velocity, $a=\dot v=\ddot x$ acceleration). Let $a=2x$. If $v$ is $0$ when ...
0
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1answer
44 views

Projectile Motion Question [closed]

A ball is thrown towards a vertical wall which is a horizontal distance $d$ from the point of projection. The initial speed is $u > 0$ and the angle of projection is $0 < \alpha < \pi/2$. The ...
1
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1answer
40 views

Moving oil out of a conical shaped tank

I need some help finishing out a Calculus problem. I'm not sure how $d$ works (single value, or integral) at the end. A conical shaped tank, with its apex pointing upward is one fourth full of ...
1
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0answers
21 views

Probability distribution obtained by repeatedly sampling $S_x,S_y$ on a spin-$S$ system

While trying to rework an upcoming quiz problem for a quantum physics course, I came up with the following question which turned out to be harder than I expected. (Note: I take $\hbar =1$ in all ...
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4answers
39 views

Airplane decelerating as a function of speed

So, I have a problem where an airplane is decelerating as a function of speed. The acceleration is described as $a=dv/dt=-0.0035v^2-3$ as a function of time. For $t=0, v=83.3$ m/s. Can someone help me ...
2
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3answers
28 views

Is the following derivation of how to find $v$ given $a=v'$ wrong?

My physics professor did the following: Let $a(t)=v'(t)$ be a given function. Suppose $v(0)$ is known, then $$ \int_{v(0)}^{v(t)} dv=\int_0^ta(t)dt \iff v(t)=v(0)+\int_0^ta(t)dt $$ I believe ...
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vote
3answers
70 views

How to solve ODE

Solve the DE: $$2y^2y''+2y(y')^2=1$$ Is it possible to solve this by implicit substitution i.e. let $v = y'$ and thus $$\frac{dv}{dy}v = \frac{1-2yv^2}{2y^2}$$ by the chain rule. And then from ...
0
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3answers
42 views

Calculation of the velocity of an object

I have the position function $$s(t) = -4.9t^2 + v_0t + s_0$$ for free falling objects. The question is what is the velocity of an object after $5$ seconds with initial velocity $120$ m/s. I tried to ...
2
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0answers
30 views

elastic strings and springs mechanics problem.

This is an example given in Edexcel M3. In question below length =1m and λ=10N but the given answer(Circled in red) it looks like the value of λ multiplied by 2. I couldn't figure it out why? Need ...
2
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0answers
27 views

Schrödinger's equation denumerable eigenvalues

The Schrödinger's equation can be written in this form: $-u''(x)+V(x) u(x) = E u(x) $ $V(x)$ is a function that is defined on the real line. We know ${u}^{2}$ is integrable on the whole real line. ...
0
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1answer
25 views

normalisation constant of SE for infinite square well

we fix arbitrary constant A by normalizing wave function $\displaystyle \int_{0}^{a}|A|^2sin^2(kx)dx = 1$ by using identity $sin^2(x) = \displaystyle \frac{1}{2}-\frac{1}{2} cos{2x}$ we can ...
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0answers
50 views

Problem with 4-body Matlab code

I'm trying to model the 4 body problem to see how Jupiter, Earth and Mercury orbit the Sun. I found a two body script and adapted it as accordingly to modify my problem, but for some reason the ...
0
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2answers
26 views

Proving That Even Potential Leads to Even or Odd Wavefunction

if the potential $V(x)=V(-x)$ (is even), then $\psi(x)$ can be taken as even or odd $\displaystyle -\frac{\hbar^{2}}{2m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)=E\psi(x)$ is the same as $\displaystyle ...