# Tagged Questions

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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### What kinds of motion obeys a higher order form of angular motion?

Angular velocity $\vec{\omega}$ can be defined in terms of velocity $\vec{v}$ and position $\vec{s}$ as: $$\vec{\omega} = \frac{\vec{s} \times \vec{v}}{\left\lvert s\right\rvert^2}$$ Constant ...
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### Show a beam is in equilibrium given the stress tensor

Having some trouble with this: https://gyazo.com/0835bdaa8e01cb976765aac94555f6ef I know how to show that at x_2 = -h the surface traction is zero, but I'm not sure how to show it's in equilibrium? ...
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### Unique ground state of Schrödinger Operators

I'm reading a book and there is an argument that the ground state of a Schrödinger operator is unique. The problem is I think the argument is complete non-sense! These are lecture notes by Witten, I ...
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### If the height of an upwardly thrown ball can be approximated by $h(t)=h_0+v_0t-\frac{g}{2}t^2$, what is $\frac{h(t_2)-h(t_1)}{t_2-t_1}$ conceptually?

I know that it describes the secant through $(t_1,h(t_1))$ and $(t_2,h(t_2))$, but I wouldn't know how to interpret it in "real life" terms. I also know that if $t_1$ tends towards $t_2$, I get the ...
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### Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
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### Dissipation term in wave equation

If we're given a string with mass density $\rho$ in units $\frac{M}{L^3}$ with constant cross-section $A$, tension $T$ in units $\frac{F}{L^2}$, and whose length is $L$; and then we assume that the ...
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### Ellipsoid moment of inertia matrix

Some background info: torque $\tau$ is defined as $$\tau = I*d\omega$$ Where $I$ is the moment of inertia matrix and $d\omega$ is an object's rotational acceleration. As I understand it, the inertia ...
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### Calculate position with increasing acceleration.

So if calculating the change in an object's position (with a constant acceleration) is done with this equation: $o = vt + (\frac12)a t^2$ $o$ is offset from original position $v$ is starting ...
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### Parabolic slide

Given a friction-less slide $y=x^2$, place a particle on the slide at $(1,1)$. The particle is acted upon by constant gravity $g= 9.8$ units/s/s. At what time does it reach bottom? The ...
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### Modeling population density with PDE

If we know that the population density $u(x,t)$ in some lake varies as a function of $x>0$ and time $t$, where $x$ increases downwards with depth, and that the population diffuses with constant $D$ ...
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### Vector Force Application

I have this question for Math StackExchange Site. Suppose you would like to cros a $132 ft$ -wide river in a motor boat. Assume that the motorboat can travel at $7.0mph$ relative to the water and ...
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### Writing PDE in the form of convervation law

What does one need to know in order to write $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+\frac{\partial^3 u}{\partial x^3}=0$ in the form of a conservation law, which contains the ...
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### Why don't more celestial bodies exhibit higher-order rotations?

It is well known that the Earth spins on its axis. It is also well known that the Earth's axis also precesses, i.e. spins around a secondary axis, much more slowly. Less well known is that we have ...
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### Computate the commutator $[p^n,x]=-ihnp^{n-1}$

Computate the commutator of $[p^n,x]=-ihnp^{n-1}$. With $p=-ih \frac{\delta}{\delta x}$ the impulse operator. $h$ stands for $\frac{h}{2\pi}$. Answer: I do it with induction over $n$. For $n=1$ it ...
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### Two trains and a fly using the series

I'm having some difficulties dealing with this problem: A train starts travelling from A towards B. It's velocity is v. Simultaneously train starts travelling at the same velocity from B to A. The ...
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### Pendulum loss/gain of time per day given : $\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$ and max displacement $5^{\angle}$

Here is what i am given: The oscillations of a pendulum are described by the equation: $$\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$$ where $\phi$ is the angle between the pendulum and the vertical axis, $l$...
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### calculate the speed of a ball, with a laser

I'm doing a project where I have to calculate the speed of a ball, passing a certain point. I want to do this with a laser, by taking the time the laser is broken in comparison of the ball it's size. ...
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### Approaching a Trajectory Problem

I am trying to design a railgun simulation. The idea is that the user can supply a starting point and velocity vector for a launcher and for a target, and the launcher will find the angle to launch ...
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### Heat problem with an internal source of heat for which the maximum principle doesn't hold.

Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it... u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
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### $\frac{\omega}{2\pi}\int_0^{\frac{2\pi}{\omega}}\frac{\sin^2\theta \cos^2\omega t}{(1+\beta\cos\theta \sin\omega t)^5} dt$

I'm going to write out the whole problem as it is given to me (bad grammar and all) even though some of the info may be irrelevant to finding a solution. A charge $e$ moving along a straight line ...
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### Uniform current in cylinder and straight wire causing same magnetic field?

The tridimensional version of the Biot-Savart law says that the magnetic field generated at the point $\boldsymbol{r}\in\mathbb{R}^3$ by a tridimensional distribution of current defined by the current ...
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given a projectory equation of the form $y=y(x)$find the curvature radius as a function of $x.$ a projectory equation , hence $x=x(t)$, input that in y and we get $y=y(x(t))$, which is what one ...
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### Instantaneously at Rest. What does it mean?

What is instantaneously at rest? Does it mean that velocity and acceleration must be both 0? So for question, $v(t) = 3 - t/2$, $t>4$, why is $t=6$ instantaneously at rest?
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### The Virasoro-Bott group and the KdV equations

The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group. For the famous $KdV$ equations these equations are given on the Virasoro-Bott ...
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### Finding the work done, given a function.

A heavy metal 2 pound bucket initially is filled with 10 pounds of paint. Immediately after it is filled, it is pulled up at a steady rate to the top of a building 30 feet high. While being pulled, ...
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### What does it mean to use levi civita symbol with Poisson brackets in this way

I'm doing some studies in mathematical methods for physics and I came across something that I don't really understand. I have only been using the $\epsilon_{ijk}$ when I cross some vectors or ...
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### Calculus Compress Spring

I have a question I cannot seem to get correct and am looking for some help. Suppose a force of $40~\text{N}$ is required to compress a spring $3~\text{cm}$ from its equilibrium length. How much ...
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### Numerical solver for maxwell equations?

Just curious if someone has come across a package where I can simply solve the basic maxwell equations(just the curl equations). I'm just interested in solving it on a 2-d plate out of interest. ...
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### How much does water cool in 1 second

I'm wondering if I've done my calculations correctly because the units I get are really weird... So.. I'm calculating how much the temperature change in $1$ second if the temperature difference is \$...