System Definition and 1000 Threads

Problem statement: Consider a fermionic system with two states 1,2 with energy levels \epsilon_i, i=1,2 . Moreover, the number of particles in state i is n_i = 0,1 . Let the Hamiltonian of the system be H = \sum_{i=1}^2 \epsilon_i n_i + \sum_{i \neq j} U n_i n_j Here, U > 0 is a...

Hello! I am stuck at the following question: Show that the wave function is an eigenfunction of the Hamiltonian if the two electrons do not interact, where the Hamiltonian is given as; the wave function and given as; and the energy and Born radius are given as: and I used this for ∇...

We express such equations by $$\frac{dx}{dt} = \beta - \gamma \cdot x$$, t denotes the time. In this case, γ depends on x, thus the dynamic equation should probably be: $$\frac{dx}{dt} = \beta - \gamma(x) \cdot x$$ 1. Setting the equation to 0 leads to two different cases: If x < K: xST = γlow...

I am a 21-year-old from Mexico that recently dropped out of engineering. I was dissatisfied by the mayor and the education system here in Mexico. I am looking forward to studying Physics in Germany because it is free and life is not so expensive. But I have my doubts. Is education at top...

I am looking to do control for a swerve drive for FRC, and I would really like a linear state space representation so that I can formulate my MPC as a Quadratic Program. I understand that in order to do this I need to find an appropriate Koopman invariant subspace, ideally finite dimensional...

I don't have too much of a clue of how to begin the problem. I first wrote the angular moementum of the system of particles: →M=∑mi(→ri×→vi)M→=∑mi(r→i×v→i). Then I know that the angular momentum from of the moving reference frame would have the velocity as the sum of the velocity of the frame...

Distance is d=1/0.07 = 14.3 parsecs The Doppler shift of one star is, Δλ = 512 - 512.04 = -0.04 So the radical of the velocity of the star is = (-0.04/512) x (3.00 x 10^5 km/s) = 23.4km/s which is the same for both stars because they have the same mass. This is as far as I've got.

From my understanding, the root locus is only concerned with open loop gain. I figured this means you would ignore the negative feedback loop and calculate the root locus from just the plant's function Workings: zeros: -1 poles: 0, -2, -2, relative degree = 2 => 90-degree asymptotes meeting...

If I have a composite system, like a two particle system, for exemple, I can construct my Hilbert space as the tensor product of the hilbert spaces of these particles, and, if ##\{|A;m \rangle \}## and ##\{|B;n \rangle \}## are basis in these hilbert spaces, a basis in the total hilbert space is...

The spring constant of a helical spring is 28 N mñ1. A 0.40 kg mass is suspended from the spring and set into simple harmonic motion of amplitude 60 mm. i use the equation 1/2 change in extension times by force where the force i assume is mass times by 9.8 but the mark scheme uses 1/2 kx ^2 and...

Find the general solution to the system of differential equations $\begin{cases} y'_1&=2y_1+y_2-y_3 \\ y'_2&=3y_2+y_3\\ y'_3&=3y_3 \end{cases}$ let $y(t)=\begin{bmatrix}{y_1(t)\\y_2(t)\\y_3(t)}\end{bmatrix} ,\quad A=\begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & 1 \\...

Moment of inertia for a rod rotated around one end is 1/3ML^2 using the parallel axis theorem Moment of inertia for a sphere is 2/5 MR^2 Itotal=Isphere+Irod=2/5MR^2+1/3ML^2 However, the answer is 2/5MR^2+1/3ML^2+ML^2 Why is there an extra ML^2 added to the moment of inertia?

determine their general solution and give a system of fundamental solutions. use the different techniques of diagonal, diagonalizedable, or triangular. $\begin{cases} y'_1 & =3y_1 \\ y'_2 & =2y_2\end{cases}$ set matrix $A= \begin{pmatrix}0 &3\\0 &2\end{pmatrix}$ then find...

Solve the system $$Y'=\begin{bmatrix}2 & 1 & 0 \\0 & 2 & 1 \\ 0 & 0 & 4 \end{bmatrix}Y$$ subtract $\lambda$ from the diagonal entries of the given matrix and take det: $$\left| \begin{array}{ccc} - \lambda + 2 & 1 & 0 \\ 0 & - \lambda + 2 & 1 \\ 0 & 0 & - \lambda + 4...

does pressure in a compressed air system increase when going from a 2" air line to a 1" air line.

nmh{383} 307.27.3 Solve the system $$Y'=\begin{bmatrix} 1 & 3 & -3 \\ 0 & 1 & 0 \\ 6 & 3 & -8 \end{bmatrix}Y$$ ok how do we get Y

Hi all, I need to convert a cooling fixture from a weighted system to a plate and bolt system. I'd like to use 4 - 10mm cap screws and a pressure plate to replace 7.82kg of weight. The weights are 190mm x 70mm of contact area. The pressure plate will have flanges to accommodate the bolts...

PART B ONLY: The cylinder undergoes torque when the mass m2 is removed: τNET = Iα = FNETr = 45α = FT(0.5) FT = 90α, therefore msystem = 90 kg After this step, I am not sure what to do. τ = ΣF = Fg - Ft = ma = (20 kg)(9.8 m/s2) - (90α) = 196 -...

The system is in rotational equilibrium and therefore experiences no net torque, meaning all individual torques must add to zero. τNET = 0 = FFTsin(θ)L - FgL - Fg(L/2) τNET = 0 = FTsin30°(0.6?) - (0.5)(9.8)(0.6) - (2.0)(0.6/2) My only problem (I think) is figuring out what the length L is for...

so far I have found the velocity 1 and 2 by dividing the volume flow rate over the area which I got from pi x dia squared/4 my v1 = 1.01859m/s and v2= 2.82942m/s i have then figured out a pressure for the 15mm pipe which i got an answer of 2.71 bar however i am stuck on the rest of the question...

In light of the modern definition of what is a coordinate system, namely it's a pair (U, f) with U a region of a m-dimensional manifold, and f a bijection from U to ##\mathbb R^m##, can we say that the polar coordinates on ##\mathbb R^2## are a coordinate system? I was thinking about this and...

Homework Statement In A spring mass system , the spring stretches 2 cm from its 's frelength when a force of 10 N is applied . This spring is stretched 10 cm from it's free length , when a body of mass m = 2 kg is attached to it and released from rest at time t = 0 . Find the A) force constant...

Hi PF! I have a tricky problem that I'm trying to model, and none of the typical textbook examples cover this--or they only cover it tangentially--so I was hoping to get some insight here. (Couldn't find a "Thermodynamics" section of the forums so if there's a better place to post this, please...

If the distribution of elements in the universe is also the distribution of elements in the solar system for regular matter, and being dark matter so overwhelmingly prevalent in the universe, why can't we see it overwhelmingly in the solar system?

Hi. After some study, I came across symmetrical components. I found the attached schematic below on the internet, and will use it to explain my question. Question: Imagine that a single-line to Earth fault occur in one of the phases, i.e. resulting in an unbalanced system (we assume it was...

It is known that the center of mass of an isolated system will assume the same location no matter what internal forces there are (as long as no net external force occurs). My first question is if there exist two bodies of masses m1 and m2 in some space that has no friction, gravity, or...

Homework Statement I am carrying out a regression for diameter of a part Homework Equations Diameter = -0.0531052 + 0.0443237 * exp (-0.0103633 * 'Time elapsed') if diameter is -0.052 then can some one please calculate the value for time elapsed would you please explain the steps The...

Hi PF! Given the ODE system ##x'(t) = A(t) x(t)## where ##x## is a vector and ##A## a square matrix periodic, so that ##A(t) = A(T+t)##, would the following be a good way to solve the system's stability: fix ##t^*##. Then $$ \int \frac{1}{x} \, dx = \int A(t^*) \, dt \implies\\ x(t) =...

Homework Statement A block is suspended by an ideal spring of the force constant K. If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is X then, find the value of X. Homework Equations mg + F = XK + K(mg/K)...

Homework Statement I have a question about the pulley problem in the attachment. Homework Equations This question can be answered using equilibrium of forces, namely Fx = 0 and Fy = 0. The Attempt at a Solution The answer key states that for the sum of the x-components, we should use the...

Hi! I'm working in a new area and I'm looking for inputs/suggestions for relevant factors to look into and possible ressource where I can read about this :) I did some tests in a pulley similar to the one below. I had a fixed weight at M2. I started with M1=M2 but added weights to M1 until...

Homework Statement I need to solve a system of two equations for T and θ algebraic and with all the other parameters known. φ is equal to: Homework Equations The relevant equations are the two equations left of * in the image below The Attempt at a Solution I tried Gauss elimination but I...

x_0\cos(\phi) = 2.78 x_0\sin(\phi)=2.78 \left( \frac{\gamma^2/2}{ \sqrt{10-\frac{\gamma^2}{4}}} \right) x_0e^{-15\gamma} \cos\left(30\sqrt{10-\frac{\gamma^2}{4}}-\phi\right)=1 I don't know awsner of \phi , x_,\gamma

Homework Statement [/B] I have a metal disc adhesively bonded at its edges to a piezoelectric ring. The piezoelectric ring vibrates radially which leads to the plate vibrating transversely. I am looking to work out the resonant frequency of the metal disc which I believe will depend on the...

Homework Statement Homework Equations F = ma The Attempt at a Solution I couldn't draw the freebody diagram. There's this weight of mass m, which is mg, downwards from m and there's tension T to upwards. This T affects mass M in the +x direction, but how could i find out the normal force...

Hi, I have a question regarding the tragic crash of the latest 737 Max. Is it not a huge error in the flight laws and the MCAS software to execute a nose down maneuver at any altitude? Should the system not have a rule to prohibit such a maneuver below a minimum altitude threshold? I'm also...

Homework Statement Hi to everyone, I'm studying thermodynamics, especially I'm focused on the work exchanged by a system. Book's explanation says that when the system received a force from the environment [F(e-s)] (on its surface) it reacts with a force from the system to the environment...

Hi everyone, I am researching how numerical simulations have evolved over the years in nuclear reactors for assessing the thermal hydraulics inside the reactor core. I have found vague information in regards to the three different main numerical techniques but want to learn more. So far...

Hello, I'm having a problem with this system. Ignore the physics. I have the feeling it should be tremendously easy... but I can't figure it out. I don't know how to extract it from the pdf so I'll post just the these 2 pages. https://ufile.io/39ovq The equations are (1.14) and (1.15), the...

Hello, I am attempting to expand my physical understanding of some engineering principles I’ve learned during my first semester of ChemE. I am making a small plastic car that will be propelled with a weak fan. I am attempting something similar to a ChemE project car. Is there a way I can use a...

**Reposting this again, as I was asked to post this on a homework forum** 1. Homework Statement Hi, I am trying to solve this math equation (that I found on a paper) on finding the variance of a noise after passing through an LTI system whose impulse response is h(t) X(t) is the input noise...

Homework Statement Given the picture: Make the free body diagrams of each body and the pulley. Remember that there are two different strings therefore there are two different tensions.Assuming that the mobile of mass M starts from rest and has a displacement D at a time t, and the bodywith...

Homework Statement (It should be noted that the actual problem has specific values associated with a, b, and c. However, at this point I'm trying to find a method to solve the problem rather than a specific solution). Homework Equations The Attempt at a Solution When I was trying to solve...

Hi, I am trying to solve this math equation on finding the variance of a noise after passing through a system whose impulse response is h(t) X is the input noise of the system and Y is the output noise after system h(t) if let's say variance of noise Y is σy2=∫∫Rxx(u,v)h(u)h(v)dudv where...

Hello my fellow scientists! This is my first post on this forum, but most certainly not my last. I am relatively new to physics. I mean, i understand the basics. I would like to make it my hobby. You know, really find a passion for the physics. BTW, i am from the Netherlands, so please do not...

Homework Statement A capacitor consists of two large metal disks placed a distance ##s## apart. The radius of each disk is R ## (R \gg s)## and the thickness of each disk is ##t##. The disk on the left has a net charge of ##+Q## and the disk on the right has a net charge of ##-Q##. Calculate...

Homework Statement Two charges, ##-q_1## and ##q_2## are fixed in the vacuum and separated by a distance ##a##. What should be the velocity ##v## of a particle with mass ##m## and charge ##q##, traveling from an infinitely far point along the line which unites ##q_1## and ##q_2## in order to...

Homework Statement Could someone look through my work? The parts where I wrote (??) are steps I am especially unsure about. Many thanks in advance. A large reservoir at temperature ##T_r## is placed in thermal contact with a small system at temperature ##T##. They end up at temperature...

What are the precise conditions for thermodynamic equilibrium? I know that a system in thermodynamic equilibrium must have constant temperature and that there can be no net macroscopic flow of energy or matter. However, is it possible for there to be a system in equilibrium that has a spatially...