System Definition and 1000 Threads

Hello, I'm a highschool student and there has been this question bugging me ever since my physics teacher insisted my point of view was wrong but it never sat right with me so I want to share it and get a proper explanation. Consider a perfectly isolated system containing an infinite mass of...

Proof: Consider the system ## \dot{x}=y(y-x), \dot{y}=x^2 ##. By theorem, Bendixson's negative criterion states that there are no closed paths in a simply connected region of the phase plane on which ## \frac{\partial X}{\partial x}+\frac{\partial Y}{\partial y} ## is of one sign. Let ##...

My attempt. I think it might be that I solve the diophantine equation wrong, according to my anwer key it should be I do not get a particular solution that is close to 397 as you can see.

I thinking of high Q oscillator examples* and pondered planetary orbits. The oscillators I am familiar with all shift energy either from place to place or different forms (mass-spring, L-C, E-B, etc.). But a planet in orbit (let's say circular) has potential and kinetic energy that never really...

I'm studying for an exam and I was checking old exams so I could practice, and I found this question that make me feel like I don't know anything: "Explain in which cases ▲x > dx and give a graphical example." I have always been taught derivatives with the typical graph with the tangent and the...

For this problem, My solution is to find the characteristic equation of the system by putting the system into a matrix. This gives ##\lambda^2 + 2f \lambda + f^2 + 1 = 0## Then each eigenvalue is ##\lambda_1 = -f - i## and ##\lambda_2 = -f + i## I then want to find the Jacobian, however, I...

My working is , Consider case where the there are two linearly independent solutions ##x'(t) = c_1x' + c_2y' = A(c_1x + c_2y)## ##(x'~y')(c_1~c_2)^T = A(x~y)(c_1~c_2)^T## Then cancelling coefficient matrix I get, ##(x'~y')= A(x~y)## ##Φ'(t) = AΦ(t) ## by definition of 2 x 2 fundamental matrix...

For this problem, I am confused by the term below. I get all their terms, expect replacing the highlighted term by ##e^{3t}##, does someone please know whether this is yet another typo? Thanks!

For this problem, My working is, ##0v_1 + 0v_2 = 0##, however, does someone please know why the example says we cannot choose ##v_1 = (0, 0)## since from ##0v_1 + 0v_2 = 0## ##v_1, v_2 \in \mathbb{R}## i.e there is no restriction on what the vector components could be)? Thanks!

Question 1: Determine the number of possible microstates for the combined system. My answer: 12 microstates. Question 2: Suppose we have a system composed of two subsystems that have reached thermal equilibrium after being allowed to exchange heat and energy. Given that the total energy of the...

Please note that the system is not in equilibrium, and that tension must be solved for the instant where the angle is 154 degrees. My attempt (correct ans is Ft = 626N)

Wasn't sure where exactly to post this. It isn't a homework problem. I am studying for my Fundamentals of Engineering exam and am struggling with control system problems. Can someone tell me where exactly the origin is on a Bode Plot? I understand the general concept of poles and zeroes but I...

I got an alert yesterday for a post by stefanoquattrini. Here's a screenshot showing it, where I've long-pressed it so you can see the URL. Note that it says "quoted your post". But physicsforums.com/posts/7060332 quotes Sagittarius A-Star, not me. The link in the post's quote header says...

This is fine but i have my own approach as follows; ##\begin{pmatrix} -7 & -6 & -12 & -33 \\ 5 & 5 & 7& 24 \\ 1 & 0 & 4 & 5 \end{pmatrix} ## → Row 1 times 5 and row 2 times 7... ##\begin{pmatrix} -35 & -30 & -60 & -165 \\ 35 & 35 & 49& 168 \\ 1 & 0 & 4 & 5 \end{pmatrix}## →...

I want to emphasize that I am not familiar with general relativity. Consider a system of particles with masses ##m_i## in gravitational field of another body ##A##. Total gravitational force exerted on ##A## will not be $$\sum G \frac{m_i m_A}{r^2}$$ where ##r## is distance between system and...

Obviously the mechanical energy of the total system remains the same. But I'm having a hard time determining of the ME of the planet is constant or if it is changing.

Well different microcontrollers act differently on a system. A pure P microcontroller reduces the error and increases the final value , a pure I microcontroller nullifies the error and increases the final value and a pure D microcontroller increases the error and keeps the final value the same...

Question image: The question should be solved by conservation of mechanical energy.( I assume surface density##\sigma## and acceleration due to gravity##g=const.##)Therefore: $$PE_i+KE_i=PE_f+KE_f$$ The axis of rotation ##PQ## is line of zero potential. Then 1) ##PE_i=\int Fdy## Since...

Hey, if I take two objects for Example the Earth and Moon and treat them as a gravitational bound “system”. The Earth and Moon have their own local curves in spacetime. Can I use/treat the whole “system” as a curve in spacetime? For example, a curve that includes all objects of the “system”...

I was given a problem to use an array, not a matrix, to solve a system of equations. I have not heard of doing this and can not find any reference to how to do it. like... 2x+3y = 12, and 3x-4y = 14 How is this solved using an array or grid?

I think its critically damped by looking at the graph of the solution.

The solution is given. What makes this solution unique is that there is a net turn for the disk. The note of the solution mentions this system is non-holonomic. My question is that are there other non-holonomic examples. What makes this particular set up non-holonomic? Thanks!

Please see the attempt sketch. Basically I have four very inefficient DC motors all commonly turning a single drive shaft at the center of the system. Currently these motors that are 2.47% efficient individually able to produce 5 newton meters of torque at 28 RPMs. So my question is this. If I...

[Mentor Note -- Two threads on the same by the OP have been merged into one] I'm having trouble understanding the solution my professor gave me, in particular, the accelerations of m_2 and m_1. When my professor solved for the acceleration of m_2, he used a as the acceleration but when I look...

Is there any documentation of the ban point system

Hey everyone, I have an attempt at fully solving this problem (my final pressure is ##p_f = 5373,64 hPa##, final temp. is ##T_f = 303,15K = 30C##), but this exercise confuses me very much. First, I have not used the masses in my calculations and I'm pretty sure my prof. accidentally copypasted...

Answer: The energy of a system with H and Cl atoms at varying distances can be represented by a curve that shows the potential energy of the system as a function of the distance between the two atoms. At very large distances, the potential energy is zero because there is no interaction between...

Lately it seems my Windows 10 computer been getting more and more sluggish. Checking on the task manager, it appears that the disk usage almost constantly stays at 100%, and that the System task is the biggest consumer. It is backing out applications I am using at the time. Is this normal...

According to this, The heat added to the system is proportional to the mass. Does someone please know how that highlighted statement is so? I think it is because the heat increases the internal energy of a system and internal energy is the sum of the translational, rotational, and vibrational...

For this, Is it possible to calculate the time it takes for the initial antinode at the string vibrator to become a node in the transient phase of the system? Also do we assume that once the system has reached steady state, that the mass has such a large inertia that it is stationary so acts as...

Hi guys, Can you give me some feedback on whether my calculation is correct? I applied the formula below (Boltzmann Distribution) but I didn‘t know what to use for the variable z. I don‘t even know if I used the correct equation. Can you help me further? The task is: Consider a system of...

https://www.scientificamerican.com/article/a-number-system-invented-by-inuit-schoolchildren-will-make-its-silicon-valley-debut/

Recommend the best out of the bunch. I am visual learner so book with lots of pics, codes would be immensely useful.

In Cohen-Tannoudji page 423, they try to teach a method that allows to find the eigenvectors of a 2-state system in a less cumbersome way. I understand the steps, up to the part where they go from equation (20) to (21). I understand that (20) it automatically leads to (21). Can someone please...

hi,everyone! if i have a 3-level system,like this： now,i want know how to measure the two-photon detuning in this system,and i‘ve known that,Δ2 and Δ3 are the two- and on-photon detunings,like this paper said: my questions are below: 1.how other researchers measure these two parameters? they...

I started by summing the forces and torques to get: - ma = mg-T - I*alpha=Tr I then used a=alpha*r and I=Mr^2 to combine the equations and solved for angular acceleration equals 81.75rad/s^2. Plugging this back into a torque equation I got that the net torque is 1.04Nm. However, the problem...

Hello! I have a 2 level system with a dipole moment d. I want to simulate numerically the evolution of the system under an external sinusoidal electric field (far off resonant). This is straightforward using SE. However I also have on top of that another electric field, created by a coupling of...

I'm seeking some reassurance I've understood the question since there are no answers given in the book and I'm getting a bit tied up in knots. What I am struggling with most is there are three per unit values for impedance already noted on the diagram without qualifying what ##Z{base}## is or...

Dear People, I have a question. I have a rotating tube like a line that has two end and one of them is the center of rotation (like a watch arrow just tube), and inside the tube a mass that is moving towards the center of rotation. So the masses moving along the line aka along the length of the...

Same instruction was given while finding value of 'g' by a bar pendulum. In the former case,does the spring obeys hooke's law while it forms a coupled harmonic oscillator system?Does the bar pendulum somehow breaks the simple harmonic motion(such that we can't apply the law for sumple harmonic...

Hello! I have the following Hamiltonian: $$ \begin{pmatrix} 0 & -\Omega\sin(\omega t) \\ -\Omega\sin(\omega t) & \Delta \end{pmatrix} $$ where ##\Delta## is the energy splitting between the 2 levels, ##\Omega## is the Rabi frequency of the driving field and ##\omega## is the frequency of the...

Hello everyone, I am a student doing an internship at IMEC, Belgium. I am studying a fan driven by a motor. This fan-motor system goes into resonance at a control frequency of 36.2 Hz. This corresponds to 18.1 Hz impeller frequency. The operating range of this fan is 30 to 40 Hz, so we can't...

Let ## \mathbf{x''} = A\mathbf{x} ## be a homogenous second order system of linear differential equations where ## A = \begin{bmatrix} a & b\\ c & d \end{bmatrix} ## and ## \mathbf{x} = \begin{bmatrix} x(t)\\ y(t)) \end{bmatrix} ## Now to solve this equation we transform it into a 4x4...

Preface We know that, in Cartesian Coordinates, $$\nabla f= \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} + \frac{\partial f}{\partial z}$$ and $$\nabla^2 f= \frac{\partial^2 f}{\partial^2 x} + \frac{\partial^2 f}{\partial^2 y} + \frac{\partial^2 f}{\partial^2 z}$$ Generalizing...

Hi All, I have got as far as below, would anyone be able to go over this, I am a little confused with plotting this out onto a graph post equation Any help would be appreciated, I am hoping to get better understanding before I move onto the next question 4 = 10 (1-e^-t/5) t = -T in (output...

выбранный контур контура и получившаяся система также показана на фото.

Looking at the given values, I thought the specific heat formula could be used to calculate the final temperature of the air: c = Q/mΔT. Since the final temperature is the sum of the initial temperature and the change in temperature, the formula can be rearranged to ΔT = Q/m*c. Q = 30 W * 10 s...

TL;DR Summary: Solar sytem forces on Unity Hello ! For my last year in my school, I've got a project to do, and I wanted to recreate the Solar system with forces on Unity. My forces are Velocity and Acceleration (I'm using the Frenet's formulas). I'm sorry I'm not a physicist and that's why...

In quantum mechanics if I repeat a measurement of the same observable in succession I get the same quantum state if it is not a degenerate state. If I make the system under consideration interact with another quantum system and meanwhile keep measuring it what happens? Does the system not...