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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0answers
24 views

Kinematics of gravity in a non uniform field

I am a first year physics student. I am trying to figure out how to compute position in terms of time for an object falling through non uniform gravity towards the earth, and by extension towards any ...
0
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0answers
6 views

How to solve a factorized Helmholtz equation?

I am reading a paper on optics an in appendix A2 they split the Helmholtz equation into two parts and write down the solution for one of those parts (link). Helmholtz Equation where the Laplacian is ...
0
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1answer
35 views

Inverse of a 3x3 matrix error!

I have this 3x3 matrix $$E_{ij} = g_{ij} + \bar{\epsilon}_{ijk}z^k$$ and want to derive its inverse. I know that its inverse is given by $$(E^{-1})^{ij} = \frac{1}{1+z^2}(g^{ij} + z^{ij} - ...
4
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2answers
139 views

Is Physics really a rigorous subject? [on hold]

Though I can't give a precise definition of the term rigor (or better to say mathematical rigor) but intuitively in case of mathematics one may note that when we say that 'the proof is rigorous' we ...
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0answers
12 views

What is the difference between initial launch velocity and launch velocity

Are they mathematically the same? If I have initial launch velocity, can I calculate time of flight and other projectile anomalies?
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0answers
18 views

Is my maths correct about Projectile Motion?

The initial launch velocity of a projectile is determined using R = 2$u^2$ / g. From this, can we calculate maximum height and time of flight if we know the initial launch velocity derived? I ask ...
2
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1answer
32 views

Charge distribution on an arbitrarily shaped conductor

From physics we know that given a charged conductor put in vacuum (no external electric fields), the charge distribution on its surface is approximately proportional to the curvature of the surface on ...
0
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0answers
12 views

Physical interpretation of the integral formula for the solution of Laplace equation with Dirichlet/Neumann boundary condition

Suppose we have a bounded domain $D$ with smooth boundary, with $G(x,y)$ being the Green's function for the Poisson equation on $D$, i.e. $G(x,\cdot)=0$ on $\partial D$ and $\Delta_y ...
4
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1answer
38 views

What are the equations modelling a vertical spring system with two masses?

Modeling a vertical spring system with one mass is a pretty common problem. I looked around online and found some horizontal spring systems with two masses, but no examples of a vertical one. I'm ...
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0answers
10 views

Calculate ratio of volumes in mixture with given ratio of masses

I have two components of a mixture: $a$ and $b$. I know that using $3.5 \text{ kg}$ of component $a$ and $0.5 \text{ kg}$ of component $b$ will give a proper mixture, and its density will equal $1.45 ...
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0answers
7 views

relation between intensity of laser and pump fluence of it. [on hold]

hi what is the relation between intensity and pump fluency? for example: Pump-Fluency =3000(micro joule/cm^2) intensity=? many thanks.
0
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0answers
35 views

Why does this graph produce a straight line? [duplicate]

When we graph the sin and cos of theta against the range of a projectile, we get a straight line. When we graph range against angle, we get a hyperbola. Why does the sin and cos of theta against ...
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2answers
25 views

Is launch speed of a projectile maximum at 45 degrees? [on hold]

I hear that range is maximum at 45 degrees, would that mean launch speed (velocity) is too?
1
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2answers
67 views

What does adding $\sin\theta \cos\theta$ make my graph a linear relationship?

What is the point of adding sin n cos of theta when graphing range? e.g. I see on hyperphysics a graph of range vs sin n cos of theta and it makes the experimental data embody a linear relationship. ...
1
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1answer
30 views

A connected path between shapes

This is a follow-up to this question: A continuous path between shapes . Let $A$ and $B$ be two measureable, bounded, connected subsets of $\mathbb{R}^2$ such that $A\subseteq B$. Does there exist a ...
1
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1answer
18 views

Wave equation in a magnetic field.

$\nabla\times\nabla\times B=\nabla(\nabla B)-\nabla(\nabla B)=-\Delta B$ since $\nabla B=0$ That seems to be odd, since one might expect $=0$ instead of $=-\Delta B$
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0answers
16 views

Calculating the errors? [closed]

Hollow cylinder of length l, inner and outer radii r1= 2.5+-0.3mm, r2= 5.5+-0.3mm, density= 7.88g/cm^(3), mass density= p, mass= (pi)xpxlx(r2^(2)-r1^(2)). What is the mass? Not sure how to approach ...
1
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2answers
37 views

Solving physics problems as a regular math problem. Why can we ignore units altogether?

If I'm solving differential equations like $Lq''+Rq'+\frac{q}{c}=V(t)$ or in general any kind of physics based problem. I can proceed to solve it as if there were no units involved and all that ...
0
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1answer
27 views

Conservation of momentum 1-D problem: track is not level

This problem is a standard 1-D problem. You have 2 equal carts approaching each other and collide on linear air track. BUT the person setting up the track did NOT do a good job at making the track ...
0
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0answers
8 views

Number of zero eigenvalues of hessian matrix corresponding to physical system

We construct a hessian from second derivatives of an energy function to find the minima of a potential energy surface and normal mode frequencies. I'm currently updating some of the implementation ...
1
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2answers
31 views

Acceleration from Velocity

How would you find the acceleration of an automobile at $t$ seconds from the formula giving velocity $v(t)$ in $ft/sec$: $$v(t) = \frac{85t}{6t+16}$$ $5$ seconds ? _____$ft/sec^2$ $10$ seconds ? ...
0
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0answers
13 views

Green's Function of second diff equation

How can I calculate the Green's function of following equation ? $$ G(r,z|r_0,z_0)? $$ $$ \frac{1}{r}\frac{d}{dr}\left(r\frac{dE}{dr}\right)+\frac{d^2E}{dz^2}+\left(k_0^2-\frac{k_x^2}{r^2}\right)E=0 ...
0
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0answers
9 views

d'Alembert Solution of wave equation for open end problem

in d'Alembert Solution of wave equation for open end problem,i saw boundary condition as $u_x(0,t)=0$,but i didn't understand why this is like that,then i saw in one book as force at free end is ...
2
votes
1answer
74 views

Tough second order differential equation

I can't figure out this diff equation (in cylindrical coordinate). How can I solve it ? Any comments appreciated $$ \frac{1}{r}\frac{d}{dr}(r\frac{dE}{dr})+\frac{d^2E}{dz^2}+(\epsilon_0 ...
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0answers
17 views

How can I find out displacement and acceleration using differential equation? [duplicate]

I know It is a duplication. I was confident that I could do this. But, I tried many times but failed to calculate the correct answer. This is what I posted before and someone answered it nicely. ...
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1answer
20 views

Calculate $\int_l^0\frac{-F \tan \theta }{2}dy$

I recently encountered the following integral to calculate the work done by a force over a distance $y$. I won't mark down the whole exercise because it is not the point of my question here. It is ...
2
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2answers
81 views

Find $t$ in $i = 50\sin\left(120\pi t -\frac{3\pi}{25}\right)$ where $i = 25$

An alternating current generator produces a current given by the equation $$i = 50\sin\left(120\pi t - \frac{3\pi}{25}\right)$$ where $t$ is the $\text{time}$ in $\text{seconds}$. (Q) Find ...
0
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2answers
32 views

Center of mass Double Integral?

Can you help me with this problem? Find the center of mass of a lamina whose region $R$ is given by the inequality: $$|x|+|y|\le 1,$$ and the density in the point $(x,y)$ is : ...
1
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2answers
71 views

Finding greatest value of a trigonometric expression involving two angles

A particle is projected up a plane inclined at an angle $b$ to the horizontal, the angle of projection being $a$ above the horizontal. Part 1: If the initial speed of projection is $V$ m/s ...
1
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0answers
23 views

Gyro drifting by time

I'm want to use a gyro which gives rotational velocity and to integrate it to get the angle. I was told that this can't be done due to the problem of drift. I was trying to understand why is this ...
3
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0answers
30 views

Fourier transform of $\frac{1}{r}$ (Coulomb potential)

When calculating the Fourier transform of a function of the form $f(\vec{r}) = \frac{1}{4 \pi \left|\vec{r}\right|}$, one encounters the problem that the resulting integral does not converge, i.e. ...
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0answers
13 views

Please help to understand a proof that any Galilean transformation can be written as composition of three (standard) transformations

I'm trying to understand one line I saw in a proof that any element of the Galilean group (i.e. any Galilean transformation) on the canonical ($\mathbb R \times \mathbb R ^3$) Galilean space can be ...
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0answers
19 views

Proof a Dirac structure may be given as $\mathcal{D}=\{(f,e)\in\mathcal{F}\times\mathcal{F}^*|\exists\lambda$ s.t. $f=Je+G\lambda,\ G^Te=0\}$

Here the definition of a Dirac structure is as follows. A subspace $\mathcal{D} \subset \mathcal{F}\times \mathcal{F}^* $ is a Dirac structure iff $\left<e|f\right>=0$ for all $(f,e) \in ...
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1answer
39 views

heat equation with perfectly insulated end

In one of my tutorial question about $1$-dim heat equation,a question about heat equation with pefectly insulated end at $x=0 $ and $ x=l$ with $u(x,t)$ as temperature function,TAs used as perfectly ...
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1answer
23 views

A ball that is thrown upward.

A ball is thrown upwards from a point on the ground, with an initial velocity $v_0$. the ball is affected by earth's gravity, and force of fraction with air that depends on the velocity of the ball. ...
0
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1answer
43 views

Mathematical problem with solving a physics issue

The power absorbed by the BOX in the Fig.A is $p(t) = 2.5e^\left(-4t\right)$ W. Compute the energy and charge delivered to the BOX in the time interval $0 < t < 250$ ms. So let me show ...
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0answers
17 views

Work done with variable mass - Vector Calculus

So Jerry was going up a hill carrying wire and laying the wire out in a spiral as he ascended and he weighed $200$ lbs and the wire went from $40$ lbs at $1600$ ft left to $0$ lbs at $0$ ft left ...
0
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1answer
24 views

center of gravity of a machine sitting on springs

Suppose we have a machine sitting on two springs $k_1$ and $k_2$ where the distance from $k_1$ to the COG is $\ell_1$, and for $k_2$, $\ell_2$. When we displace the the machine downward, the right ...
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1answer
59 views

Is possible to determine the biggest number in universe? [closed]

Since i graduated in high school, i think about a maximum number. I'm not a mathematician. My point is: If we have a range of digits, let's say 5, the biggest number it will be 99999 of course, then ...
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0answers
33 views

problem about heat in thermodynamics

$$\nabla G=-T\nabla S-T\nabla S_{sur}=-Q+q $$ $$\nabla G=-T\nabla S-T\nabla S_{sur}=-(U-W_{rew})+q $$ $$\nabla G=-T\nabla S-T\nabla S_{sur}=-(q+W-W_{rew})+q $$ $$\nabla G=-T\nabla S-T\nabla ...
0
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1answer
39 views

re-writing a mathematical expression

I am reading the following paper: http://www.nova.edu/ocean/Physics/PDF/Solovievetal2007.pdf and am trying to write a MATLAB program to solve equation 1.26, which is shown as: $$ K_{int} = ...
1
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1answer
54 views

Cauchy Momentum Equation - Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
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3answers
54 views

Derivative with physics

The position $s$ at time $t$ of a moving object is given by $$s(t)=\frac{1}{3}t^3-\frac{3}{2}t^2$$ Assume the object moves in a straight line and that $t$ is greater or equal to zero. Measure $s$ in ...
3
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1answer
77 views

Differential Equations Question involving a spring-mass system

I'm working through a Differential Equations book and came across a question that puzzles me: "Consider a spring-mass system where there are two masses connected in series by springs, with each ...
3
votes
1answer
83 views

Find one of two forces, given their resultant

The resultant of two forces acting on a rock is 107N and it makes an angle of 38 degrees, and 40 minutes with the first force of 51N. Find the magnitude of the second force and the angle it makes ...
0
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1answer
58 views

An arbitrary guy needs some advice! [closed]

I am doing Mechanical Engineering (2nd year) and it's already becoming clear that I am no more interested in this course.I am very much motivated to study Theoretical Physics and Pure Mathematics(I ...
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0answers
19 views

Soft ceiling game physics

I'm making a game that has physics. For now, I have a implemented drag and thrust (upwards acceleration): $ a_{t+1} = a_{th} (1 - (v_t / v_T)^ 2) $ (acceleration) $ v_{t+1} = v_t + \Delta t \space ...
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0answers
27 views

Check : What i have done is correct or Wrong ? I just want to assure my answer

Ali leaves home for school at 12 mph .Twenty minutes lather his father leaves him at a rate of 36 mph to reach him at a rate of 36 mph. How fast must he drive before he gets Ali?? Ali : S=VT ...
0
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0answers
23 views

Setting differential of independent variable to Zero

Consider that we are dealing with magnetostatic field (constant magnetic field) $B=B_1$ and $\frac{dB}{dt}=0$. The values (of $B=B_1$ and of $\frac{dB}{dt}=0$) are maintained by nature from the ...
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0answers
25 views

Lubrication Theory: Quick Question!

Basically, I'm modelling the flow of a "coating" process -- a fluid flow between a flat moving plane and a stationary cylinder, 2D, cartesian coordinates. Subscript 0 is the at the minimum height b/w ...