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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how to solve this integral involving any square root

how to solve the integral $\int\sqrt{\alpha+\beta e^{\gamma t}}dt$ i got this integral from the problem Given that the velocity $v$ of a body $t$ segonds after passing a point $O$ is found by ...
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1answer
21 views

Simple Harmonic Motion Formula

The SHM general formula is this: $y(t) = A\sin(\omega t + \alpha) +B$ I have two questions about it As far as I know, there is the cosine formula for when the particle starts at P and sine for ...
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3answers
53 views

Where have I gone wrong? A basic question in physics (Mechanics)

A stone is dropped vertically in a velocity of $15$ minutes per second, from a point $40$ meters above the ground (excuse my poor English.). a. How long will it take to the stone to hit the ground? ...
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1answer
16 views

Is $Cr^a\hat r$ always a conservative vector field?

Is the vector field $\vec r(r, \theta, \phi) = Cr^a\hat r$, where $C, a\in \Bbb R$ are constants and $r \in \Bbb R^+ \cup \{0\}$ is the radial component, always a conservative vector field? I really ...
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1answer
13 views

Matlab, given data in matrix form 550x2, need to find the period of signal [on hold]

By using Matlab, I have adata in matrix form 550x2, need to find the period of signal by finding two maximas and finding difference between their x-axis location.
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1answer
34 views

Finding speed of snowballs given initial velocity and angles

You and a friend stand on a snow-covered roof. You both throw snowballs from an elevation of $14$ m with the same initial speed of $12$ m/s, but in different directions. You throw your snowball ...
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2answers
34 views

is there any mathematical model how the guitar strings are related?

I'm just curious to know the mathematical relationship between guitar strings and how their frequency changes with the variation of guitar's string length and thickness. Say, I'm vibrating some node ...
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1answer
22 views

When should I recalculate starting values for my physics engine's multistep integration?

I'm writing a physics engine that uses an Adams-Bashforth and Adams-Moulton predictor-corrector pair for integration, and Runge-Kutta 4 to calculate starting values for their initialization. I am ...
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3answers
319 views

Solve for velocity, if acceleration is a function of velocity?

Yes, this is a canned question, because canned questions are simply solvable to understand ideas. No, this is not homework. For simplicity, let's assign values. A given object weights 1000 kg, it ...
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3answers
24 views

A $1.00 m^3$ volume of iron has a mass of $7.86 \cdot 10^3 kg$, find the length of one side with a mass of $200g$

So this is a relatively simple physics problem, but I'm sort of stumped and need some help finishing this off. The full problem reads: Iron has a property such that a $1.00 m^3$ volume has a mass ...
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1answer
19 views

Acceleration vector at highest point of accelerated projectile [on hold]

A projectile is thrown at an angle of $60$ degrees with horizontal with initial speed $20 m/s$,with H being the highest point of its trajectory.Another particle P is now forced to move along the same ...
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2answers
26 views

Strange formula for radar horizon, does anyone know where it comes from

I am in Electronics Technician "A" School in the Navy and we are learning the basics of radars. In one module, we were exposed to this formula which confuses me. If someone has an inkling as to why it ...
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1answer
25 views

Spaceship transit times [on hold]

I want to travel X km. My ship can accelerate at 1 G for half the distance, then needs to decelerate at 1 G for the second half. What's the formula for determining the transit time?
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1answer
15 views

Expression for $dW$ for a 3D position dependent force $\vec{F}(\vec{r})$.

I was looking at the derivation of the infinitesimal element of work done for a 3d position dependent force and I couldn't get over the switching of $\text{d}\vec{v}$ and $\text{d}\vec{r}$ in the ...
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1answer
14 views

Little mistake with Levi-Civita symbol property

I have this equation $ \varepsilon_{ijk}B_k = \partial_iA_j - \partial_jA_i $ and I was asked to prove $\mathbf{B}=\nabla\times\mathbf{A}$, where $\mathbf{B}=B^i\mathbf{e}_i$ and ...
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1answer
46 views

Planetary Motion: A comet describe a parabola about the sun [on hold]

A comet describe a parabola about the sun, show that the sum of the squares of the velocities at the extremities of a focal chord is constant. I have no idea how to solve. Please help. I only ...
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0answers
38 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $? [migrated]

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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1answer
14 views

Rearrangement of harmonic oscillation formulae

Can anyone show me why the following identity is true? $$A\cos(\omega t) + B\sin(\omega t) = \sqrt{A^2+B^2}\cos\left(\omega t + \arctan\left({ \frac BA}\right)\right) $$ I ask this is relation to ...
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2answers
20 views

Calculate work done using integral

A chain lying on the ground is 10m long and its mass is 80kg. How much work is required to raise one end of the chain to a height of 6m? So im working in MKS system since its m and kg so the work ...
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1answer
25 views

Inequality involving sums and products (related to multi-stage rockets)

Let $a_i$ and $b_i$ be strictly positive real numbers for $i=1,\ldots, n$. I wonder whether the following inequality holds in general or does not:$$\frac{\sum_{i=1}^n a_i+\sum_{i=1}^n ...
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1answer
24 views

A Problem On Vectors-Forces

A particle is subjected to two equal forces along two different directions.If one of them is halved,the angle which the resultant makes with the other is also halved.The angle between forces is ? Ok ...
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2answers
29 views

At 2:00pm a car's speedometer reads 30mph, and at 2:10pm it reads 35mph. Use the Mean Value Theorem to find an acceleration the car must achieve.

I'm only assuming that f(a) and f(b) are assigned to each respective velocity, but I'm not sure how the mean value theorem can be applied to distance rate and time.
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30 views

How do you get the curvature tensor of the Schwarzschild Solution?

So, on the Wikipedia page on the derivation of the Schwärzschild solution , I get everything up to the part about the Ricci tensor. What were the components of the tensor that were used? Could ...
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2answers
56 views

Need help with integral to evaluate electric field around a spherical shell.

I was trying to prove that the electric field at a distance $x>R$ from the centre of a charged shell is $\dfrac{kQ}{x^2}$. I did the physics part but I got stuck when I encountered the following ...
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31 views

Identities with dirac deltas

How are you supposed to verify or derive common physics text 'identities' involving dirac deltas like $$ \lim_{t \to 0} \mbox{sign}(t) \frac {\partial}{\partial t} \frac{\partial}{\partial x^i} ...
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1answer
15 views

Equilibrium Of Forces - Vector Condition

A body is in equilibrium under 3 forces A,B,C.Show that A x B = B x C = C x A (x represents cross product). Well I know the longish method of writing A= a i + b j + c k form and then balancing along ...
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1answer
6 views

Finding the velocity $v$ for which the total time the object moves from its initial position to the position where it stops is minimal

A body first moves with a constant velocity $v$ along a track with a length of $L=5 \ [m]$ and then decelerates with an acceleration $a=2 \ [\frac{m}{s^2}]$ till it stops. How to find the velocity $v$ ...
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2answers
65 views

Proof that Electromagnetic force is much stronger than gravity [closed]

The electromagnetic force is given by this formula: $$Fl=q(v\cdot\,B)$$ and gravity is given by $$Fz=m\cdot\,g$$ Now do I've to proof that the electrmagnetic force is much stronger than gravity but ...
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1answer
23 views

Application of differential equation (wave equation)

I am not 100% sure what is "steady-state solution w(x)". I tried to solve the question by first making equation (1) equals to zero; then integrate it twice with respect to x and substituted u=0,x=0 ...
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1answer
23 views

Help solving a Rectilinear Motion problem - straight roads

Problem: Amar drives 16 km directly west from Upper East Side to Central Park at a speed of 90 km/h, then directly south 8.0 km/h to 7th Avenue at a speed of 80 km/h, then finally 34 km southeast to ...
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11 views

Taylor series of Lagrangian

Take a look at the Lagrangian defined here. $L=\frac12 a(q)\dot q^2 - V(q)$. You can think of $a$ and $V$ as functions. It seems as though $L$ depends only on $q$. If $q_0$ is a point for which ...
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14 views

Moment of inertia and its perpendicular distance question.

Boundary of plate is an ellipse with semi-axes a and b. L is a line that passes through the center of the ellipse and makes angle j with the axis of length 2a. Density function is constant and its ...
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30 views

Force between two finite parallel current carrying wires

Most standard physics textbooks compute the force two infinite wires exert on each other, but they remain silent about the case where the wires are finite. Let's say we have two parallel wires ...
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12 views

Find electrostatic energy of three-parallel-plates capacitor

Question: A capacitor consists of three identical and parallel thin metal circular plates, area A, in the planes z = −H, z = a and z = H, (−H < a < H), centres on z axis, and at potentials 0, V ...
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1answer
60 views

Simple question on group theory

Suppose we have the following system of differential equations: \begin{cases} \frac{dx_{i}}{dt}=f_{i}\left(\boldsymbol{x},\boldsymbol{y}\right), & i=1,\ldots M\\ \\ ...
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1answer
26 views

How can I find out the center of mass of thin plate in the shape of a rectangle?

How can I find out the center of mass of thin plate in the shape of a rectangle ABCD If the density at any point is the product of the distances of the point from two adjacent sides AB and AD? ...
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2answers
29 views

Physics Word Problem Concerning Finding Power

A twin engine jet aircraft is climbing at a 10 degree angle at 260 ft/s. The thrust developed by a jet engine is 1000 lb. The power developed by the aircraft is ______ (2000 lb)* (260 ft/s) = ...
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1answer
36 views

Solid Angle Integrals

I'm currently working on solving a solid angle calculation for my physics project. I'm trying to solve it computationally using python - but my coding skills are basic at best. I need some hints/tips ...
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1answer
20 views

How Do You Solve for Landing Speed?

A ball is thrown eastward into the air from the origin (in the direction of the positive x − axis ). The initial velocity is 50i + 80k. The spin of the ball results in a southward acceleration of 4 ft ...
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1answer
30 views

Formula for 2 vectors

Hello StackExchange people, I have an issue. I need to create a formula to find degrees and size at a problem like the following: So I have $0-359$ degrees and a length of $2$ lines, and I need to ...
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2answers
41 views

Finding total distance and time for a bouncing ball - application of series

Problem: A ball is thrown straight upward so that it reaches a height $h$. It falls down and bounces repeatedly. After each bounce, it returns to a certain fraction $f$ of its previous height. Find ...
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2answers
48 views

Second-order nonlinear ordinary differential equation. Newton's second law.

I have this problem, I will try to give as close translation to English as possible: "A point with mass m moves towards a center due to force $m·k^2/(r^3)$, where $r$ is the distance from the center. ...
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0answers
41 views

Sum over all compositions of $n$ into exactly $k$ terms (overlaps of $SU(k)$ coherent states)

Given two $k$-dimensional vectors, $\vec{x}$ and $\vec{y}$, I would like to find, $$ d(\vec{x}, \vec{y}) = \left|\sum_{t_1 + t_2 + \cdots + t_k = n} \prod_{1\leq q \leq k} (x_q\times ...
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1answer
40 views

Why does the vector field $(\sin (\theta), - \cos(\theta), 0)$ indicate sideways motion?

If I study a physical system, such as a car, and let it drive forward a little bit, say a distance $m$, then I can draw out the right triangle and find the car's position at $(m\cos \theta, ...
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16 views

Meaning of Torricelli's Equation ($v^2=u^2+2as$)

The equation of motion $v^2=u^2+2as$ is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) ...
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35 views

partial differential equation applicational problem

As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from ...
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1answer
15 views

Find out the angular speed in terms of time.

Here is the equation that describes the motion of a planet under the gravitational field generated by a fixed star: $u=\frac el\cos\theta+\frac 1l$, where $u$ is the reciprocal of the radial distance ...
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63 views

Could you explain the failure of the Hodge decomposition to exist for non-compact manifolds?

I'm a physicist and the mathematics around the Hodge Decomposition is way formal than I can currently follow (I'm trying to better myself but it'll take a while). Specifically what I'm ...
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3answers
95 views

infinitesimal intervals in physics

The density of states of a system in an interval $[E, E+dE]$ is given implicity by $dV = D(E)dE$ (Or I suppose explicitly, by $D(E) = \frac {dV}{dE}$, but we'll be integrating it anyway, so it doesn't ...
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Thermodynamics: find exit temp and velocity of air out of a nozzle?

I don't know if I can really ask a thermodynamics question here on this math site but I need help and this was the best site for when I needed help in math class. Concerning thermodynamics, I have ...