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. anemone

    MHB Find real solutions to a system

    Suppose that $x$ and $y$ are positive real numbers. Find all real solutions of the equation $\dfrac{2xy}{x+y}+\sqrt{\dfrac{x^2+y^2}{2}}=\sqrt{xy}+\dfrac{x+y}{2}$.
  2. Hajarmq

    I Total energy of an isolated system

    If a closed system has kinetic and potential energy such as the total energy (the sum of the two) equals zero for all times, what does that mean? In other words, what does it physically mean that the total energy is always zero for a closed system? I think I have a small misunderstanding of the...
  3. phun_physics

    I Derivation of Average Square Energy Fluctuation in a Canonical System

    The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...
  4. jk22

    I Does this make a cubic out of a quadratic system?

    Suppose the system of equations (coming from invariance of the wave equation) : $$B=-vE\\A^2-B^2/c^2=1\\E^2-c^2D^2=1\\AD=EB/c^2\\B=vA\\AE-BD=1$$ If one adds a lightspeed movement like $$A=a+f\\B=b-cf\\D=d+h\\E=e-ch$$ Then solving equ 1 for f gives $$f=(b+ve-vch)/c$$ Equ 4 for h implies...
  5. Julio1

    MHB Existence of Unique Solution for Nonlinear System with Arbitrary Constants

    Show that the nonlinear system $\dot{X_1}=2\cos X_2, X_1(0)=a$ $\dot{X_2}=3\sin X_1, X_2(0)=b$ has a unique solution for the arbitrary constants $a$ and $b$. how to solve this system? Thanks.
  6. mktsgm

    Medical The Role of Antibodies in the Immune System: A Closer Look

    I have a doubt. It is said that antigens detected by macrophages and and Dendritic cells (by way of PAMPs and DAMPs) can initiate and mount an immune response, why antibodies need to be produced. Ok, antibodies opsonize the intruders. But then even without antibodies, the innate immune system...
  7. L

    Engineering Block Diagram Reduction - Control System

  8. G

    Solving the First Equation: v1, v2, & ωR

    I've marked correct answers above. Have a look at the solutions: How is the first equation justified? Shouldn't v2 and ωR be of opposite signs? What is v1? And how is it equal to v2? My biggest problem is the source of v1 since the ring is not having vertical displacement, then what is v1?
  9. H

    I Solving this system of equations in different ways

    Good night! How do I find the values of a (real) so that the solution of this system is? (i) just an ordered pair? (ii) exactly two pairs. (iii) exactly 3? (iv) is there a place where you have more than 3 pairs as an answer?So... I thought like this: I developed the first part. I solved the...
  10. S

    Distance traveled and period of a mass - spring - pulley system

    1. How will the motion of M be? I assume wire S is inelastic so will M move downwards but not in straight line? (I mean M moves downwards but because the left side of pulley is connected to S, it will be static and the right side of pulley can go down along the extension of the spring so its...
  11. H

    Calculating Period of System with Masses, R & dX

    Here is the picture on the system. I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position. In the thread...
  12. P

    Find the tension in the string of this two mass system

    I know that it will probably execute something similar to circular motion. I thought of conserving momentum but I think there is an external force being applied due to the impulse which will prevent me from doing so. I know that once I find the tension it would become very easy to find the...
  13. G

    Is Venus the key to economic success in our solar system?

    I am writing a space opera, that is meant to be hard, except some alien magic. So far, i have the following points : asteroid belt is the most valuable for rare material mining, there they live in O Neil cylinders. Travel is done by fusion ships, that can maintain miliG-s of constant...
  14. A

    Potential energy of a system of two punctual charges along the X axis

    I have not clear how to solve this problem. Here it is my attempt at a solution: Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...
  15. N

    Robust control system calculations

    can i solve this problem i didnt go university due to Covid-19
  16. Arunsaikalki

    What is the natural frequency of this system?

  17. E

    A single external force doing work on a system of particles

    Suppose we have a system of particles being acted upon by a single external force ##\mathbf{F}^{e}##. Each individual particle feels a force of ##\mathbf{f}_i = \mathbf{f}_{i}^{int} + \mathbf{f}_{i}^{e}## such that ##\sum_i \mathbf{f}_{i}^{e} = \mathbf{F}^{e}##, and ##\mathbf{f}_{i}^{int}## are...
  18. cwill53

    Mechanics Question- Massive Rope in a Pulley System

    I understand how they might have got to these answers but I'm still kind of shaky on how the mass of the rope plays a role in the tension at point B, and how to mathematically represent the tension at any point along the rope; I know the tension varies because the rope has mass. If I was to...
  19. A

    Help on how to find stellar radius with an eclipsing binary system

    My best guess right now is use Newton's version of Kepler's 3rd Law to maybe find a combined mass, as I'm under the impression that the smaller star's mass would still be too large to ignore, but I'm not confident. And I wouldn't be sure as where t go from their, either. Any guidance would be...
  20. P

    Potential energy of a System of charges

    This is my attempt the system The 1 is the initial configuration where the 3 electron is at infinity. The 2 is the final configuration where the 3 electron is midway.U1 is the potential energy between e1 and e2 U1 = (q1*q2)/(4*π*ε0 * (0.02)^2); // q1, q2 charge of electrons K1 =...
  21. aligator11

    Engineering Homework problem - Pendulum oscillatory system

    Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.
  22. E

    ABS system on a two-wheeled vehicle - Conservation of Angular Momentun

    Hello, The question I have pertains to conservation of Angular momentum on a motorcycle. I know that the dynamic friction is less than the static friction, so when you are braking on a (say a motorcycle) and the wheels lock up, the bike is bound to fall over. This is the reason ABS (Anti-lock...
  23. LuccaP4

    D'Alembert's principle on a pulley system

    This is the problem's picture: My problem is that what I got for one acceleration (m3's) via Newton's equations is not the same as via D'Alembert's principle (I've checked on my PC if they are the same expression). I can't find the mistake. Any suggestion is welcome. I attach pictures of what...
  24. tanaygupta2000

    Lagrangian of a spring mass system

    I know that from the given problem, I need to find the expression for Kinetic energy, KE = 1/2 m [r(dot)]^2 and Potential energy, PE = 1/2 k r^2 So L = 1/2 m [r(dot)]^2 - 1/2 k r^2 Hence H = 1/2 m [r(dot)]^2 + 1/2 k r^2 I assume that the fixed length r0 is provided to find the value of end...
  25. Physics lover

    Value of frictional forces in a 3-block system

    So I started by checking the options.I substituted the value of friction in the equations I got by making free body diagrams.I got different value of Tensions.For 1 and 3 Tension came to be 38 N.For 2 Tension came out to be 42N and for 4 Tension came out to be 40 N. Now I think that I will take...
  26. MathematicalPhysicist

    MATLAB A Lorenz's system of ODEs doesn't get executed in Matlab

    I use the following script and function in MatLab, but get three errors. I shall first write down the code and after that the errors that I get. function yprime = lorenz_de(t,y) %LORENZ_DE Lorenz equations. % yprime = lorenz_de(t,y). yprime = [10*(y(2)-y(1))...
  27. il postino

    Chemistry Equilibrium temperature of a water and ice system

    Equal masses of ice at –10ºC and water at 80ºC are placed in an insulated container and allowed to reach thermal equilibrium. Calculate the equilibrium temperature Data: Water(ice): 37,65 J/mol.K Agua (l): 75,29 J/mol.K ## Lf = 6011 J/mol ## I solved it this way: ## -Q_{l} = Q_{ice} ## ##...
  28. M_Abubakr

    Infinite-Extent 2D Mass-Spring System vibration and dispersion relation

    Hi, I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a. I need to try find dispersive relation...
  29. P

    Hamiltonian of this system?

    Let a mass m charged with q, attached to a spring with constant factor k = mω ^2 in an electric field E(t) = E0(t/τ) x since t=0. (Equilibrium position is x0 and the deformation obeys ξ = x - x0) What would the hamiltonian and motion equations be in t ≥ 0, in terms of m and ω?? Despise magnetic...
  30. D

    I Logarithmic terms in a system of equations

    (I hope this is not a double posting) I want to solve this system of equations, containing logarithmic terms: ##7\ln(a/b)+A = 7\ln(d/e)+D = 7\ln(g/h)+G## ##7\ln(a/c)+B = 7\ln(d/f)+E = 7\ln(g/i)+H## ##7\ln(b/c)+C = 7\ln(e/f)+F = 7\ln(h/i)+I## ##a\phi_1+d\phi_2+g\phi_3=X##...
  31. jaumzaum

    I Possibility of an integral system

    I was solving a Physics problem, and for it to be consistent there should exist a function f(t) in real numbers and a time T, such that: $$\int_{0}^{T} f(t) dt=0 $$ $$\int_{0}^{T} \int_{0}^{t} f(t') dt' dt=0$$ $$\int_{0}^{T} f(t) (\int_{0}^{t} f(t') dt') dt>0$$ i.e. the integral is zero, the...
  32. engnrshyckh

    Engineering Control system damping ratio

    I don't know how to calclute error in derivative for daming ratio of 0.5
  33. M

    MHB System no/infinitely many solution(s)

    Hey! :o We have the matrix $A=\begin{pmatrix}1 & -1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1\end{pmatrix}$ and the vectors $b_1=\begin{pmatrix}1 \\ 0 \\1\end{pmatrix}$ and $b_2=\begin{pmatrix}-1 \\ 1 \\2\end{pmatrix}$. Check if the system $Ax=b_i$ for $i\in \{1,2\}$ has a solution. If the system is...
  34. engnrshyckh

    Engineering Discover the Stability of the System through a Visualization | Learn More

    See the picture I am stuck at 12(1+2k)=0 So k=-1/2 for stability k must have value greater the - 1/2 which means there will no sign changes in rooth array and equation represents a stable system
  35. H

    I Building a coefficient matrix for a system of equations

    I want to solve the following system of equations ##M_{1} = f_1+f_2+m_1+m_2\ \ ;\ \ M_{7} = f_1+f_2+s_1+s_2\ \ ;\ \ M_{13} = m_1+m_2+s_1+s_2## ##M_{2} = f_1+f_3+m_1+m_3\ \ ;\ \ M_{8} = f_1+f_3+s_1+s_3\ \ ;\ \ M_{14} = m_1+m_3+s_1+s_3## ##M_{3} = f_1+f_4+m_1+m_4\ \ ;\ \ M_{9} = f_1+f_4+s_1+s_4\...
  36. new90

    Virtual work in a pulley system

    If 1kg make a displacement of 1unit upward then A make a 1/2unit down because 1/sin 30.after that i have no idea what do I will really need help. Thanks!
  37. M

    Engineering Mechanical Vibrations - 2 DOF System - Rod with 2 springs

    Hi, So the question is to: derive the equations of motion for the following in terms of x1 and x2? The bar is assumed to be light and rigid. (NB. I know I posted another vibrations problem earlier in which I tried to use an energy approach to get to the equations of motion. However, we haven't...
  38. jamestyler

    Thermally Self-Regulating System Setup

    I would like to design a system that is capable of generating frictional heat through its servo motor to heat up an enclosed chamber to 500 'Celsius . The challenge is that external heating source such as heating element, heat chamber etc. shall not be included in the design setup. Assuming that...
  39. batclocks

    Simplifying a two-particle system to a one-body problem

    The first part is actually fine. You just note that since r=r1+r2 that means r1=r+r2 and r2=r1-r and you substitute that into the center of mass, R, and simplify to get r1=R+(μ/m1)r, and r2=R-(μ/m2)r But the next part is where I'm very confused. The general idea is that you want to prove ∇1 =...
  40. E

    Calculating System Work and Displacement of Center of Mass

    <work done a system> a) w=5N*(0.4m)=2J I think this is right, but b) center of mass initial = ((0.5kg)(0.05m)+0.5kg(0.65m))/1kg = 0.35m center of mass final = ((0.5kg)(0.45m)+0.5kg(0.4+0.1+0.3+0.25))/1kg = 0.75m I'm not sure for this one... How can I calculate the displacement of the...
  41. E

    New unit of mass in a different system of units....

    I'm finding it slightly tricky to just get a hold of where to start. I try $$\text{m}\text{s}^{-1} = \frac{c}{3\times 10^8}$$ If we then set ##c = 1##, that would seem to imply $$3\times 10^8 = \text{s}\text{m}^{-1}$$For ##G = 1##, I might also write $$\text{kg}\text{m}^{-3}\text{s}^{2} =...
  42. snatchingthepi

    How to care about only one particle in a two-particle system

    So for the 1D infinite well with the states above, I have ## \psi_{symmetric} = \frac{2}{L} [sin[\frac{\pi x_1}{L}]sin[\frac{2\pi x_2}{L}] + sin[\frac{2\pi x_1}{L}]sin[\frac{\pi x_2}{L}]] ## ## \psi_{antisymmetric} = \frac{2}{L} [sin[\frac{\pi x_1}{L}]sin[\frac{2\pi x_2}{L}] - sin[\frac{2\pi...
  43. Eggue

    Angular momentum of a system of a rotating rod and sliding rings

    I got the correct answer for the first part but I'm not sure why the answer for (b) is the same for (a). Wouldn't the rings falling off mean that I_f = \frac{1}{12}M_L L^2 only where I_F, M_L, L are the final moment of inertia, mass of the rod and length of the rod as opposed to I_f =...
  44. H

    I How to solve a small system of non-linear equations?

    If we have the following relations between x, y, and z: M_{xy}=\frac{2xy}{x+y} M_{xz}=\frac{2xz}{x+z} M_{yz}=\frac{2yz}{y+z} where M_{xy}, M_{xz}, and M_{yz} are known constants, what technique can be used to determine the values of x, y, and z?
  45. S

    I How could a quantum system "predict the future"?

    What is nonlocality? How could a quantum system (like a superposition - is that right?) "know" an interaction will take place? Source...
  46. T

    A 11 coordinate system for separation of variables

    Good Morning I have a very vague memory of having read (about 40 years ago) that there are only 11 coordinate systems in which the field equations of physics can be separated. I can no longer be sure if my memory has failed me. But this issue has been in my head for all these years. (Gotta do...
  47. Z

    Python Displaying system information using psutil

    Hi, I am getting following error message: I have written the following code which should display the system information of a simple program which I am running as a function: import psutil import osclass Counting_SysInfo: def __init__(self, i): self.i = i def...
  48. M

    Thermodynamics Problem: Cylinder-Piston System with Friction

    Hi guys, First of all I'm sorry for my bad english I'll try to be as clear as possible. I have tried to solve this problem to understand the First Law of Thermodinamics: Q+L=ΔE_t In fact I know L (in the current convention) is the work which the envirorment does on the system but I don't...
  49. P

    Entropy and the Helmholtz Free Energy of a Mass-Piston System

    Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...
  50. Mina Farag

    Applying the implicit function theorem to a system of equations

    My attempt: According to the implicit function theorem as long as the determinant of the jacobian given by ∂(F,G)/∂(y,z) is not equal to 0, the parametrization is possible. ∂(F,G)/∂(y,z)=4yzMeaning that all points where z and y are not equal to 0 are possible parametrizations. My friend's...
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