# What is System: Definition and 1000 Discussions

A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory.

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1. ### Exam asks me for a case where ▲x > dx?

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...
2. M

### Proving stability of linear system equations

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...
3. M

### Fundamental matrix linear system equivalent to linear matrix system

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...
4. M

### Solving linear DE systems using 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!
5. M

### Finding general solution to linear system

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!
6. ### Find number of microstates of combined system

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...
7. ### How Do You Solve a Non-Equilibrium Pulley System with a 154 Degree Angle?

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)
8. ### Where is the 'Origin' on a Bode Plot?

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...
9. ### Bug Why Did I Receive the Wrong User Alert on a Forum?

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...
10. ### I Solve the system of linear equations

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}## →...
11. ### B Does gravitational force act on system or its components?

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...
12. ### Does Mechanical Energy of a Planet Change in an Elliptical Orbit?

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.
13. ### Function of PD, PI, ID and PID microcontrollers on a system

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...
14. ### Find the linear speed of the particle when system rotates about axis

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...
15. ### B Gravitational Field of a System: Exploring the Curves of Spacetime

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”...
16. ### I Using an array to solve a system of equations

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?
17. ### Modelling a spring system with damping force and external forces

I think its critically damped by looking at the graph of the solution.
18. ### Holonomic constraints and non-holonomic system

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!
19. ### Estimating efficiency of a system

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...
20. ### Confusion on mechanics problem involving cart, blocks, and pulley

[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...
21. ### Suggestion What is the Ban Point System for Posting Personal Math Theories?

Is there any documentation of the ban point system
22. ### Mixing two gases in an isolated system and calculating final p and T

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...
23. ### Chemistry Valence Bond Theory: Energy of a system with H and Cl atoms

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...
24. ### What is causing high disk usage and slowing down my Windows 10 computer?

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...
25. M

### Heat added to system increases mass

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...
26. M

### Assumptions for string vibrator system

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...
27. ### A system of independent particles (energy levels)

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...
28. ### I Number System by Inuit School Kids now in Unicode

https://www.scientificamerican.com/article/a-number-system-invented-by-inuit-schoolchildren-will-make-its-silicon-valley-debut/
29. ### Other Book to learn system administration using CentOS Linux?

Recommend the best out of the bunch. I am visual learner so book with lots of pics, codes would be immensely useful.
30. ### I Finding Eigenvectors of 2-state system

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...
31. ### A How to measure the two-photon detuning in 3-level system?

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...
32. ### Net Torque Within a Mass and Pulley System

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...
33. ### A Two level system in a thermal noise electric field

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...
34. ### Three Phase Per Unit System - Mark up, represent as single phase equiv

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...
35. ### I Question about a Rotating system with mass moving inwards

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...

37. ### I Thoughts about coupled harmonic oscillator system

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...
38. ### A Two level system under electric field without RWA

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...
39. ### Fan-motor system resonance problem

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...
40. ### I Fundamental matrix of a second order 2x2 system of ODEs

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...
41. ### B Solving for the Nth divergence in any coordinate system

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...
42. ### Engineering Open Loop system with distance-velocity lag and single transfer lag

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...
43. ### Creating a Contour System: Results

выбранный контур контура и получившаяся система также показана на фото.
44. ### Change in temperature of air in a closed system

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...
45. ### Solar System Forces -- Simulating the planetary orbits for my project

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...
46. ### I Repeated measurements on a quantum system interacting with other quantum systems

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...
47. ### I Is there a Boltzmann distribution for a system with continuous energy?

Hi. I'm not sure where to put this question, thermodynamics or the quantum physics forum (or somewhere else). For a system in equillibrium with a heat bath at temperature T, the Boltzman distribution can be used. We have the probability of finding the system in state n is given by ##p_n =...
48. ### Probability of Negative Value in Sz 1/2 Spin System w/ Lambda 1 & 2

Will the probability to provide a negative value of a Sz 1/2 spin system always be 0? If lambda 1 = hbar/2 and lambda 2 = -h bar/2 ?
49. ### I Pressure Required to Circulate Liquid in a Closed System?

Example: 3/4 pvc in closed circuit with pump. Linear distance of pipe=30ft / head 8ft .... so not counting friction, what general description of force can describe what's required to make the liquid circulate?
50. ### Pumping power calculation of a vertical closed-loop system

Hi there, I hope that somebody can help me with this.. Any response is much appreciated! Let's have a vertical closed-loop system where the fluid circulates using the pump. The temperature in both sections gradually changes (the upcomer section is heated up) so that the densities, velocities...