System Definition and 1000 Threads

Are there any standart ways to solve such systems? \[ \begin{cases} m(t, x) - f(t, x)= \int_{0}^{t} q(\tau,x) \, d\tau \\ u(t,x) = \int_{-\infty}^{+\infty} \frac{1}{2 \sqrt{\pi s t}} e^{-\frac{(x-\xi)^2}{4st}} f(t,x-\xi) \, d\xi \end{cases} \] Unknown functions are \( f(t,x) \) and \( q(t,x)...

I am not sure if i get the question... At first i would say it is impossible to give a answer, we can not distinguish. But i think if we know the phases in this instant, we can give and answer, so my answer would be: "If we know, by some reason, what are the phase in this instant, we can give...

Find all integer solutions of the system of equations $x+y+z=3$ and $x^3+y^3+z^3=3$.

The first law of thermodynamics states that the change in the internal energy of a system equals the net heat transfer into the system minus the net work done by the system. In equation form, the first law of thermodynamics is ΔU = Q − W. in the mathematical expression of the first law of...

I cannot understand the solution at https://www.aapt.org/physicsteam/2015/upload/E3-2-5-solutions.pdf, because the solution is terse and skip steps (at least i think so). I figured out that the name of this transfer is "Hohmann-Transfer Orbit". A detailed walkthrough would be appreciated. If I...

I was just wondering what is wrong with the following logic; From the Gibbs-Duhem relation we get, ##\frac{\partial \mu}{\partial P}\Big\rvert_T = v## Now consider, ##\frac{\partial v}{\partial \mu}\Big\rvert_T = \frac{\partial }{\partial \mu}\Big (\frac{\partial \mu}{\partial P}\Big\rvert_T...

Find all the real numbers $a,\,b$ and $c$ that satisfy the following system of equations: $\begin{align*}a + b + c &= 1\\ \dfrac{a}{ 1 - a}+\dfrac{b}{1 - b} + \dfrac{c}{1 - c} &= 6ac + 6bc = (a + 1)(b + 1)\end{align*}$

and this is my solution for question (d), it may seems that $$R=(k)/(k-m\omega^2)R_0$$ so that $$\omega ≠ \omega_i =√(k/m)$$ but $$\omega_c <\sqrt{k/m}$$ is always true, ##\omega_i## corresponds to the limit case when ##F_max## is infinitely large Besides, I don't know other Physics prevents...

Can't visualize how the system moves, can anyone help me?

In some experiments of a complex physical mathematical system, we found some symmetry phenomenon, very similar as symmetry breaking phenomenon, say, as translatable sysmmetry etc. These symmetry (breaking) phenomenon occurs in most of the parts of the system or some parts of the system. Can you...

FBD Block 1 FBD Block 2 FBD Pulley B I'm mainly concerned with the coordinate system direction in this problem, but just to show my attempt, here are the equations I got from the system. ##-T_A + m_1g = m_1a_1## ##T_B - m_2g = m_2a_2## ##T_A - 2T_B = 0## Using the fact that the lengths...

I am trying to design/build a large self-filling drinking station, aka water bowl, for my goats and cow (see design attached). It's a takeoff of a dog's self-filling water bowl, i.e., uses gravity and vacuum to automatically refill the bowl as the water in the bowl is drank. The rain barrel is...

In this system (consisting of just the gas) heat is transferred to the gas by means of a reservoir. So this means energy is added to the system. Does this necessarily mean that the work done on the lead shot due to an increased pressure will equal the heat that enters the gas? We are assuming...

The attached file is the coordinate system I've used a) $$\vec{E}=\dfrac{\vec{F_e}}{q}=\dfrac{1,10\cdot{10^{-13}}\hat{j}\;N}{1,6\cdot{10^{-19}}\;C}=6,88\cdot{10^5}\hat{j}\;N/C$$ b) $$\sum{\vec{F_{net}}}=\vec{0}=\vec{F_e}+\vec{F_m}$$...

In the horror novel, the Descent, by Jeff Long, Earth has a system of deep caverns so extensive that they constitute a virtual "sub-planet," a kind of partial lower deck in the Earth's crust, whose mutated human inhabitants have horns and decorate their bodies with extensive scarification...

Dear all, While simulating a coupled harmonic oscillator system, I encountered some puzzling results which I haven't been able to resolve. I was wondering if there is bug in my simulation or if I am interpreting results incorrectly. 1) In first case, take a simple harmonic oscillator system...

I was reading about systems of linear equations. Even if we have the same number of unknowns and equations, we may still have infinitely many or no solutions. But if in addition to that the determinant of the matrix of coefficients does not vanish, then does it necessarily imply that we have a...

This section of the Wikipedia article on tidal locking https://en.wikipedia.org/wiki/Tidal_locking#Mechanism states: (Note : A is the earth; B is the moon) I am having trouble understanding that last "whereas" bit (bold font). It seems to me that if we consider lower and lower rotation speeds...

I saw that the solution states that the torque about the center of mass is zero, since the man does not rotate about its center of mass. However, I then thought about taking the torque about the left foot (so the right foot for the man's POV). Hence: $$\tau_{left} = \tau_{0} + \textbf{R}\times...

If I take away the planets in the solar system and leave the sun alone, would the sun have less energy than before?

##\vec F= 2x^2y \hat i - y^2 \hat j + 4xz^2 \hat k ## ## \Rightarrow \vec \nabla \cdot \vec F= 4xy-2y+8xz## Let's shift to a rotated cylindrical system with axis on x axis: ##x \to h, y \to \rho cos \phi, z \to \rho sin \phi ## Then our flux, as given by the Divergence theorem is the volume...

The displacement of the end of a spring varies as , the block on the spring is subject to a viscous force proportional to the velocity. Spring stiffness k. (a)Find the displacement of the block: (b)When γ -> 0 First of all, i have a doubt i we could start saying the component of the force is...

Seems to me the answer is a specific vector: The second forms a plane, while the first X is just a vector. The intersection between the λX that generates the (properties of all vectors that lie in the...) plane (i am not saying X is the director vector!) How to write this in vector language?

Hello! Brand new to the forums, hopefully someone here can help me out. Paths start out at the edge of a circle and "flow" along a polar equation that determines phi based off the initial phi (phi0) and a variable radius (ie. as your radius grows, your phi is changing). Hopefully this image...

Well, i think the important here is the system, what you think about?: -2kx2 + kx1 = mx2'' -2kx1 + kx2 + kXocos(wt) = mx1'' After this, is just solve, i found: x2 = (k*xo*cos(wt)*(4k/m - 2w²))/(2m*(k/m - w²)*(3k/m - w²)) The cool is that if we put w equal the two normal frequency x2 tends to...

Stumbled across this and found it interesting. Solar System Dynamics pages at JPL (Jet Propulsion Lab)/NASA. Has Bodies, Orbits, Physical Data, Tools, etc. https://ssd.jpl.nasa.gov/?site_map Cheers, Tom

This is a problem very easy to deal with if we consider the effective spring constant, however, i want to avoid this solution, and see how to justify the period of this motion just by analyse the forces or the energy, what seems a little hard to me. First of all we would need to find the force...

Hello, I am learning about blockchain this summer. I sort of get the big idea (skipping the middle man, encryption based decentralized system where everyone that is on the database can see everybody else transactions). Isn't the fact that everyone can see any transaction unsafe and against the...

Solve the following sustem 1) x+y+z+w=22 2) xyzw=648 3) \frac{1}{x}+\frac{1}{y}=\frac{7}{12} 4) \frac{1}{z}+\frac{1}{w}=\frac{5}{18}

I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...

So in particular, how could the determinant of some general "operator" like $$ \begin{pmatrix} f(x) & \frac{d}{dx} \\ \frac{d}{dx} & g(x) \end{pmatrix} $$ with appropriate boundary conditions (especially fixed BC), be computed? And assuming that it diverges, would it be valid in a stationary...

Fp = Fg +Ff Fp = (21*9.81*sin(31)) + (0.2*21*9.81) Fp = 147.30 Fp*d = 147.3 *4.5 Wp = Wm = 662.87 = 663 J I am not sure what I am doing wrong. Should I subtract the force of friction from the force of gravity? Have I assumed that the pulling force is equal to the sum of gravity and friction...

Hi all, When I first learned about cladistics, it seemed like an elegant and objective way of classifying life - forget about subjective physical similarities, classify purely based on scientifically testable ancestry, and have all taxa be monophyletic clades, so everything in one taxon is more...

So, should i write All of these as accodring to wiki pedia maxwell applied coherence concept to FPS, CGS, and SI is already coherent so answer will be All of these ?? Am i right or MKS because question is restricted to mechanics only ?

I did some calculations for the ground state energy and wave function of a system of two electrons put in a finite-depth 2D potential well. Regardless of the shape of the potential well (square or circular), the expectation value of the electron-electron distance ##\langle r_{12}\rangle =...

In graphene system, the velocity operator sometimes is v= ∂H/ħ∂p, and its matrix element is calculated as <ψ|v|ψ>, i.e., v_x = v_F cos(θ) and v_y = v_F sin(θ) [the results are the same with Eq. 25] for intraband velocity. Recently, I see a new way to calculate the velocity matrix (Mikhailov...

This problem is very easy to solve considering that the two particles belong a closed system under action of conservatives force. My doubt is if it is possible to solve the problem by consider one particle by time, that is: Suppose that we know the particle m one is under gravitational force...

Hello PF, I am building a traction assembly for a self balancing bot project and I am having some conflict with my intuition and practical testing results. The setup consists of a motor mounted to a chassis, the shaft coupled to a wheel that rests on a surface with non-zero friction. Below...

OFFICIAL SOLUTION: d=e^(-1) mod 160=107 mp= c^(d) mod p=7 mq:=c^(d) mod q=7 MY THOUGHTS: I understand how d = 107, but I got that by using m = (17-1)(11-1) = 160. What I don't understand is the next two lines (from the official solution). I am aware of the P = C^d mod n (decryption) formula...

Solve the following :A) x^2-y\sqrt xy=126 y^2-x\sqrt xy=-63 B) \frac{x} {y}+\frac{y}{z}+\frac{z}{x}=\frac{y}{x}+\frac{z}{y}+\frac{x}{z}=x+y+z=3

solve the following system: x^2 +xy +y^2=37 x^2+xz+z^2=28 y^2+yz+z^2=19

Solve the following system of imequalities: 2x+3y-4>0 3x-4y+5>0

Hello, I have a system with 2 degrees of freedom with 2 non-holonomic constrains that can be expressed by:##A_1 dq_1 +Cdq_3 + Ddq_4 = 0## ##A_2 dq_1 + Bdq_2 = 0##Being ##q_1, q_2, q_3## and ##q_4## four generalized coordinates that can describe the movement of the system. And ##A_1, A_2, B...

Hello please be aware that my understanding of physics is basic, but I want to learn - and I will if explained simply enough please. I looked on here and found the cube in space query from last year, and I just about understood it, but the scalars and vectors did throw me, so hopefully it will...

Hello, the physical domain in the (y, z) space is mapped to a rectangular computational region in the (ŋ,Ƹ)-space, where (ŋ,Ƹ) are the new coordinates. This technique frees the computational simulation from geometry restriction. after transforming the governing equations ( PDEs) to the...

The figure represents a system composed of two ideal fixed pulleys that support three masses A, B, and C of the same mass M, suspended by light and inextensible threads. Massor A is simultaneously suspended by two wires, one connected to massor B (wire 1) and the other to massor C (wire 2). We...

Summary:: What is the force N which acts on a support point at the moment just after system is released? [Thread moved from the technical forums, so no Homework Template is shown] A light bar with m1 and m2 masses (m1≠m2) at the ends placed on the support point (in the middle of the bar)...

I have done question 1. But I'm struggling with the other one. So since the only thing I know about the rocket is the mass and the velocity, I guess I have to use momentum to solve this problem. From the first question, I found out that the x-velocity of the projectile is ##v_x=5...

The following is an improved version of my previous post https://www.physicsforums.com/threads/falling-electric-dipole-contradicts-the-equivalence-principle.964594/ Consider the following system comprising a particle on the left with charge ##+q## that is a large distance ##d## away from two...

I am a bit confused on the definition/convention of work. In some books I see statements that say : "If work is done on the system, its sign is positive. If work is done by the system, its sign is negative." And in other books I see things like: "By convention, work is regarded as positive...