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Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tags instead.

2
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1answer
28 views

Simple equation that will recreate this graph shape?

I am working on an audio synthesis project for a guitar, and one of the most challenging parts has been finding an equation so the decays of the partials (modes) can roughly match the behavior of real ...
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0answers
24 views

Understanding Expansion: shorthand in Sandia doc

enter image description here https://www.osti.gov/servlets/purl/10194662 It has been too long since I studied math. 68 years old. Trying to decrypt the math in an old 1994 ballistics study. per ...
0
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1answer
26 views

Evaluating the argument of a complex expression

I am trying to verify a relationship presented in this paper. I want to verify that the argument of $$\frac{E_{2}}{E_{1}}=\frac{r-\tau\exp\left(i\varphi\right)}{1-\tau r\exp\left(i\varphi\right)},...
0
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1answer
43 views

differential equation - spring

2y'' + 5y' + 3y = x + cos(x) Given that the differential equation represents a mass on a spring with friction, qualitatively rate the spring as weak or strong (in relation to friction). Justify your ...
0
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1answer
24 views

calculating friction with momentum and stopping time [on hold]

The question I'm having trouble with is: What is the momentum of a 90 kg person on ice skates that slides 4 m/s across the frozen pond? The person skids into the cattail remnants and stops in 3 s. ...
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0answers
37 views

Is the derivative of T(t) over the magnitude of T(t) always the unit normal vector?

If you have an equation $$r(t)=\langle 1,\cos(t),\sin(t)\rangle$$ then $$r'(t)=\langle 0,-\sin(t),\cos(t)\rangle $$ and $$\|r'(t)\|=\sqrt{\sin^2(t)+\cos^2(t)}=1$$ thus $T(t)=\langle 0,-\sin(t),\cos(t)\...
0
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1answer
57 views

Author's derivation of time-independent form of Maxwell's equations

Laser Electronics, 3rd edition, by Joseph T. Verdeyen, gives the following: To describe an electromagnetic wave, we need two field-intensity vectors, $\mathbf{e}$ and $\mathbf{h}$, which are ...
0
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2answers
46 views

Calculating x% faster than y?

I'm working on an app as a little side project, I can handle the code no problem but I can't get my head around some (fairly basic) math right now. So, I need a formula, please. The easiest way I ...
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0answers
31 views
1
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1answer
31 views

How can I properly force this “object” to follow the indicated path

I'm working with drones and I want them to follow a path. This is the current behavior (black is the path, red is the drone): As you can see, it goes to the destination point (C), but it doesn't ...
2
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1answer
37 views

How does this entropy equation simplify?

This is from the bok "Pattern Recognition and Machine Learning" By Bishop. I am having a hard time following the last step of this equation Where Stirlings approxaimation is subtituted for $\ln N!$ to ...
2
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1answer
29 views

Series convergence in quantum statistical mechanics

I'm asking my question here and not in physics SE for the fact that, even though the result comes from physics, the problem I'm having is more mathematical. Calculating the heat capacity for roto-...
0
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1answer
24 views

Integral of equation of motion for pendulum

I am reading a book on pendulums and at some point during the derivation of the period of the pendulum, the authors jump from one equation (I) to another (II). I would be really grateful if someone ...
1
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0answers
26 views

Fluid mechanics differential equation

I have a problem stated as the following: $$\frac{p+B}{p_{atm}+B}=\left(\frac{\rho}{\rho_0}\right)^N\tag{1}$$ And I need to find the pressure at a depth of $10,000m$. We can do this by using the fact ...
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0answers
16 views

Euler Lagrange Equation with co-/ contravariant Tensors

I am currently trying to show the following equation which, appears from the Euler Lagrange equation: $$\frac{\partial}{\partial \partial_{\nu} A^{\mu} } \left( \frac{1}{4} F_{\mu \nu} F^{\mu \nu} \...
4
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0answers
129 views

Is Leibniz integral rule (basic form) allowed in this (physics) improper integral? Why?

Electric potential at a point inside the charge distribution is: $\displaystyle \psi (\mathbf{r})=\lim\limits_{\delta \to 0} \int_{V'-\delta} \dfrac{\rho (\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|} dV'$ ...
0
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1answer
27 views

magnitude of unknown force on wall bracket question

I'm really stuck with part b of this question, even where to start. I think I keep over complicating it. If anyone could help that'd be amazing!
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0answers
33 views

Finding the equilibrium between two beads with equal and opposite forces connected by a spring

Imagine two beads each on parallel rods. The beads are connected to each other by a spring of stiffness $k$. The beads each exert an equal and opposite force $F$ to each other. The distance between ...
0
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1answer
23 views

Line integral of a conservative vector field which has a potential - Issues factoring derivatives

Let $F = −\nabla \phi$ be a conservative force field. Suppose a particle of mass $m$ moves in this field. If $A$ and $B$ are any two points in space, prove that $$ \phi(A) + \frac{m}{2} v_A^2 = \...
0
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2answers
34 views

Find Free Fall Time with Integral

"You are standing on a cliff, ready to jump into the ocean. The ocean is 30 feet below you. What is your velocity as you hit the water?". I know that I can solve it with $Δx=0.5at^2$, and use $t*a$ ...
2
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1answer
39 views

When are phase space flows induced by the Hamilton equations homeomorphisms?

Suppose I have a certain Hamiltonian of a system, with the corresponding Hamilton equations. The equations induce a certain flow in phase space. Since each point in space has a certain trajectory ...
1
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1answer
26 views

Why the relation $\mathbf{E}=-\nabla \psi$ holds at points $P \in V'$?

Let there be a continuous charge distribution in space having volume $V'$ and density $\rho$. Let: $\displaystyle \mathbf{E}=\int_{V'} \rho\ \dfrac{\mathbf{r}-\mathbf{r'}}{|\mathbf{r}-\mathbf{r'}|^3}...
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0answers
9 views

Numerical solution of a locally Lipschitz differential equation. (Gross-Pitaevskii)

A (very simplified) version of the GP-equation, can be written as $\frac{d\alpha}{dt}=-Ui\alpha^*\alpha^2=-Ui|\alpha|^2\alpha$, Where $i$ is the imaginary unit. In contrast to what I first thought, ...
1
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0answers
41 views

Finding the angle at which a ball should be thrown to pass through a given coordinate

A man standing at the origin of a coordinate system throws a ball with the initial speed $v_0 = 15$ m/s from a height of $1.4$ m. The throw is made at a 60° angle in the $xz$-plane and a $-15°$ angle ...
0
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1answer
40 views

Evaluate the change in the potential energy

If the force $$F=3i +4j $$ moves a body from the position $$A(2 , 3)\ \mathrm{to}\ B(7 , 6) $$ .Evaluate the change in the potential energy of the body . My turn: The work done by the force =$$(3,4) •...
0
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2answers
25 views

Determine the forces exerted by the supports on the pipes at contact surfaces. [closed]

The question is: Three smooth homogeneous cylinders A, B, C are stacked in a V shaped through as shown in the figure below. Each cylinder weights 100 and has a diameter 5 cm. Determine the forces ...
1
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0answers
19 views

Solving second order DE's with respect to parametric equations

I am looking at the motion of particles in force fields (so acceleration). With a given vector acceleration $$\vec{a}(x,y)= \begin{bmatrix} P(x,y) \\ Q(x,y) \end{bmatrix} \textrm{with initial ...
0
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1answer
97 views

Any way to find a closed form expression, or to simplify this summation?

While solving a certain physical problem, I have reached the following summation: $$S = \sum_{k = 0}^n \left({n-k-\frac{1}{2} \choose n-k}\right)^2 \ \ \frac{(k+l)!}{k!}$$ where $n, k$ and $l$ are ...
1
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2answers
41 views

indefinite integral of 1/x where x is dimensional?

As we know, the integral of $\frac{1}{x}$ is $ln(x)+c$. Because $x$ and $dx$ have the same dimension, $\int\frac{dx}{x}$ is dimensionless. But my problem is: $x$ is dimensional. I've been trained that ...
2
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2answers
56 views

Show that $\int_{0}^{2\pi}\frac{dk}{2\pi}\,e^{-s(e^{-ik}-1)+ikm}=\frac{s^{m}}{m!}e^{-s}$

Book (Altland and Simons, Ch 10, Eq. 10.41) I am reading used the integral: $$\int_{0}^{2\pi}\frac{dk}{2\pi}\,e^{-s(e^{-ik}-1)+ikm}=\frac{s^{m}}{m!}e^{-s},\quad m\in\mathbb{Z},\, s\in\mathbb{R}.$$ ...
2
votes
2answers
40 views

Squared modulus of a complex expression

I am trying to verify a formula that was presented in a paper giving the intensity transmission of a resonator. I need to confirm that the squared modulus of $$\frac{r-\tau\exp\left(i\varphi\...
0
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0answers
34 views

Solving and making sure

There is a particle in a system.The mass of this particle is M=0.5 kg. The initial and final velocity are V0=2i , Vf=2j (i,j denote the unit vector in x, y axes) Question: 1) The initial and final ...
0
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1answer
9 views

Determine the resultant using triangle method - Analytical Method - Vector Quantity - Physics

I'm having some problems finding the resultant in my physics subject. So heres the given problem: A = 10 meters B = 20 meters 30° The graph looks like this: A is in between Q1 and Q4 in x axis the ...
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0answers
9 views

Finding the optimum parameters for volumetric swept 3D display application utilizing planetary gear system

Imagine a planetary gear system as below: There are two curved screens attached to a shaft of the planet (little purple gear). The curves are logarithmic spirals. So they are rotating with the ...
1
vote
1answer
25 views

Infinitesimal approximations in triangle yielding differing results

I am trying to prove the equations of motion of a pendulum from its energy equation, and I am obtaining different results depending on which infinitesimal approximation I choose. The idea here is to ...
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0answers
19 views

The magnitude of the acceleration? The tension in the lightweight cord?

Unfortunately I don't know anything in this question When two objects of unequal mass ( $m_1<m_2$ ) are hung vertically over a frictionaless pulley of negligible mass, the arrangement is called an ...
0
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1answer
27 views

How to use the condition that $\vec a_i \cdot \vec b_j=2\pi\delta_{ij}$ to find reciprocal lattice vectors, $b_j$, for this rectangular lattice?

Consider a rectangular lattice in two dimensions with primitive lattice vectors $(a,0)$ and $(0,2a)$. Which of the following are reciprocal lattice vectors for this lattice? (a) $\quad\dfrac{...
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0answers
25 views

Proofing equation containing time-ordering operator

Preparing for a presentation at university (I'm a Bachelor physics student) I have come across the formula below containg the time-ordering operator $T$. Although i have now understood the action of ...
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0answers
34 views

cell division and Banach–Tarski paradox

I know it is really not formally well stated, but is there a way to formalize the non-equilibrium process of cell division using notion/formalism/variation of Banach-Tarski paradox? Maybe somehow ...
1
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0answers
27 views

notation in derivative multivariate function - partial and total derivatives in physics

Let $f(x,y)$ is sufficiently smooth for all I write and let $x=x(t)$ and $y=y(t)$. I am curious about a proper notation of derivatives. Given the limit definition of a partial derivative, I would say:...
2
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1answer
19 views

Determine the magnitude and direction of the electrical field

Consider a positively charged infinite slab with uniform charge density $\rho_1$ and thickness $4a.$ This slab is oriented such that the two faces of the slab are located on the planes $x=-2a$ and $x=...
0
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1answer
32 views

finding velocity of a leaking object in motion

I am having issue with my working for the problem displayed below. Here are my working as follows The questions ask for newtons second law, now as the mass varys with time I use the momentum form ...
1
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2answers
49 views

Calculating Launch Angle Given Distance with Added Height (which itself depends on launch angle)

In my physics class we have learned to calculate a desired launch angle to allow a projectile to hit a target given the target’s distance away and the initial velocity. Now in this case the initial ...
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0answers
64 views

Applying math incorrectly to physics

I have the following argument in physics which I'm pretty sure is wrong: Since all change in location is bounded by the speed of light times elapsed time, we can conclude that any movement is $c$-...
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0answers
76 views

The integral over a sufficiently large volume should vanish

I was recently reading an article about organized waves in turbulent flows. At one point in the theoretical part of the study, the author presents the equations for the kinetic energy of the organized ...
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0answers
23 views

Proof of $\sum_{i=0}^{N_s - 1} e^{-j2\pi n(k'-k)/N_s} = N_s\delta(k'-k)$

Currently, I'm faced with this problem: Prove that this property holds when $N_s$ is an even integer, for any integers $n$, $k'$, $k$: $\sum_{i=0}^{N_s - 1} e^{-j2\pi n(k'-k)/N_s} = N_s\delta(k'-...
8
votes
1answer
94 views

In frictionless rigid-body collision dynamics, what happens when a ball falls into a crevice where two planes intersect?

When a ball bounces on a horizontal plane, its vertical velocity $v$ gets negated and multiplied by a coefficient of restitution $\varepsilon<1$, and its horizontal velocity $u$ is unchanged. The ...
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votes
2answers
41 views

Separation of variables and integration

I also have that $\rho(t_0)=\rho_0$ and $a(t_0) = 1$. I'm trying to separate the variables here to reach the desired solution, with my working as follows: \begin{align*} \frac{\dot{\rho}}{\rho} &...
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0answers
19 views

Error with generators of Lorentz group (basis of Lorentz Lie algebra)

Can someone help me figure out why my $J_y$ is incorrect? :/ It's supposed to be \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & -...
0
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2answers
22 views

Derivation from complex simultaneous equations (transmission of a resonator)

I am trying to verify a derivation presented in a journal article, where the authors derive an expression for the transmission of a lossy fiber ring resonator. They start with the equations: ...