System Definition and 1000 Threads

I was asking myself what is the definition of a Cartesian Coordinate System. Can we say that it's a coordinate system such that - the basis vectors are the same ##\forall x \in R^n## - the basis vectors are orthonormal at each ##x \in R^n## So for instance, normalized polar coordinates do not...

Homework Statement Derive an expression for the angle alpha and determine the initial horizontal and vertical forces exerted at the point of attachment of the bell rope to the plank. The system is in static equilibrium Both ropes are light ie negligible mass. The point of attachment has been...

Let's say I have a service that publishes events, like eo ("Bought 100 shares of AAPL") e1 ("Bought 100 shares of T") e2 ("Sold 500 shares of TSLA") and there exist stateful services subscribing to the events and whose state depends on the events being processed successfully and in the correct...

Homework Statement How to apply constraints in the system to get a relationship between the displacements of block of mass m and pulley of mass M.? Homework Equations ∑T.a= 0 The Attempt at a Solution Assuming tension in both strings to be T . -T × a1 ( for the block) + 2T × a2 ( for the...

There is remarkably little information on the internet including Wikipedia on this topic. Can someone point me in the right direction as I want to build a visualization software that illustrates the supergalactic plane and the coordinate system with any kind of celestial sphere involved. All I...

hello everyone 1. Homework Statement Problem: An AB beam, loaded with a distributed load q (KN/m), the length of the beam is 2 m. EI=constant find the reactions in the beam ,we use y''=-(1/EI) *M(x) Homework Equations y''=-(1/EI) *M(x)[/B] The Attempt at a Solution first we have 6 reactions...

Hi. We tried to make some quantitative measurements with a Pasco ripple tank system, a video camera and software for video analysis. We generated circular waves and tracked the propagation of a crest, from which the software computed the phase velocity: We used 5 Hz, 10 Hz and 20 Hz...

I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>? A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...

I am stuck on like the first page of thermal physics. It seems like the signs of the work done on the system are opposite when the volume is expanded and compressed. But when I imagine myself pushing or pulling the piston, I get confused from W = \textbf{F}\cdot \textbf{d} This work will be...

Hello, I am a food truck owner and I recently had a situation which made me rethink my power needs for my kitchen on the food truck. I have a 2001 Workhorse forward control Stepvan and I wanted to run an alternator, batteries, and an inverter setup INDEPENDENT of the trucks own alternator and...

Hello all, I've been entrusted a project of developing a Vacuum Drying System for my company. This system will be used for instant drying of automotive parts after washing. Needless to say the parts will be wet and at an elevated temperature (approx 50 degree C). The requirement is to dry the...

Homework Statement c is the coefficient of damping, k is the spring constant, and m is the mass. if the cart is displaced from rest by distance X_0 and released at t=0 with initial velocity v_0=1.Homework EquationsThe Attempt at a Solution Ok this might be a stupid question because I wasn't...

Does our solar system host a Ninth planet, If so has our solar system under gone planetary migration?

Hello everyone, this is my first post here so please excuse me if its in the wrong area. I am looking for the tabular approach to solve a complex gear train based off the spur gear differential design. Attached is a photo of the differential. The requirements of the necessary differential...

This thread is a shoot-off from this thread. Assuming some relation between human language and logical reasoning, how would this relate, let's say, to the arrival and evolution of logic in human and animal psychology? I would presume that some logic, for example classical logic, can be more or...

Homework Statement I have a project to make the Solar system on Python, which I have done, but they also require from us to calculate the total energy of the system. We don't have to make the orbits of the planets elliptical, they should be circular and I believe I made them like that. Since...

Greetings! Hey, can anyone help me? I need an explanation how can Lyapunov help me to check the system weather it is chaotic or not. Let say I have this equation Rossler System Eq.(1) So how can you tell that the system have chaotic behavior or not? Does it depends on parameters? or from...

I've moved to a "new" house - built about 350-400 years ago. Firewood in a stove kind of works for heating a few rooms, but not the full house. So far it seems like the grid power tends to die about twice a month. Temperatures is expected to reach -25C (-13F) for the coldest couple of weeks...

Homework Statement A particle of a mass ##m## is embedded in a circular rail, (radius: ##R##), without any friction. In a given moment, the particle finds itselfs without velocity at point C, and a force is applied on the rail, which starts moving with an ## \vec A ## constant acceleration. Use...

Homework Statement Calculate the natural circular frequency ωn of the system shown in the figure. The mass and friction of the pulleys are negligible. The diagram is attached. Homework Equations ωn = (k/m)1/2 The Attempt at a Solution I can see the total mass of the system is 3m. So in the...

I have a dual boot laptop: Windows 7 and Ubuntu. I would like to format my laptop, and install a fresh copy of Windows 7, and install the new version Ubuntu 18.04.1 LTS. My question is: do I need to do any thing special? Usually, when I start my laptop I press one of the F keys (I forgot which...

Imagine there is an radiation concentrator (winston cone) surrounded with extremely many layers of foil for radiation insulation, except at the smaller opening. Every part of the setup is initially in thermal equilibrium with the surroundings. The amount of thermal radiation flowing through the...

Homework Statement Homework Equations unreliable source of solution: The Attempt at a Solution [/B] I came across this problem while practicing for the final exam in thermodynamic,my attempt: i recall this type of problems are not steady-flow system. Since the change in kinetic and...

Salutations, I'm starting in statistical mechanics and reviewing some related studying cases I would like to understand what occurs in small systems with normal modes of vibration, for example, a small system that has 2 normal modes of vibration, with natural frequencies $$\omega_1$$ and...

Homework Statement I have to calculate the critical points of the following system. $$x'=cx+10x^2$$ $$y'=x-2y$$ The Attempt at a Solution So I solve the system $$cx+10x^2=0$$ $$x-2y=0$$ So if $$x=2y$$ I have $$2yc+10*4y^2=2yc+40y^2=y(2c+40y)=0$$ and I get $$y=0$$ and $$y=-\frac{c}{20}$$ f I...

I have been reading up on clear-air pulsed radars and am wondering if it is possible to scale down a large radar system to one with reduced power and gain, but also greatly reduced range. Here are the specs for a large radar: Output power = 2.5 mega Watts Antenna gain = 47db. Range = 15km. If...

Homework Statement Determine whether the following system of equations has a single point of intersection. If so, find the point of intersection. 4x+y-9z=0 x+2y+3z=0 2x-3y-5=0 Homework Equations n1⋅(n2×n3) The Attempt at a Solution I have to pick a variable, use a pair of equations to...

Homework Statement Find the tension in each section of string in terms of ##θ_1##,m and g. Homework Equations Equilibrium of force,dimensional analysis of force. The Attempt at a Solution The support points are at rest and in each points,there are two equal tension force acting in opposite...

I have a project to make the solar system. I am trying to start from somwhere. On the notes it says that we need to start by creating a System of Particles Two-body simulation (Circular motion) Implement Gravitational acceleration Each particle (planet) could have its own field. I.e. Each...

Consider the classical scenario a stone falling in the Earth gravitational field. Classically we attach a Potential Energy to the stone and using the law of conservation of (mechanical) energy we are able to evaluate the dynamic of the falling stone. This model assume a stone in a "external"...

Hey! :o We have the basis $B=\left \{\begin{pmatrix}1 \\ 1 \\ 1\end{pmatrix},\begin{pmatrix}2 \\ 1 \\ 0\end{pmatrix}, \begin{pmatrix}1 \\ 2 \\ 1\end{pmatrix} \right \}$ of $\mathbb{R}^3$ and the vector $v$ can we written as a linear combination of the elements of the basis as follows...

Hello, $\vec{x'}=\small\begin{pmatrix}1&2\\3&2\end{pmatrix}\vec{x}+t\small\begin{pmatrix}2\\-4\end{pmatrix}$ Now i got the solution to this differential equation system as...

Homework Statement [please see attached photo] Homework Equations [please see attached photo] The Attempt at a Solution [please see attached photo] The issue for me starts with (but probably doesn't end with) replicating the velocity equation using the Conservation of Energy equations. Is...

Hi All. I'm new here so I hope you will bear with me and please tell me if this is out of context or in the wrong part of the forum. I am trying to programm a falling pipe system with corners in ArchiCAD (GDL). I have been programming in different languages for a while now, but new to 3D vector...

Homework Statement I'm having trouble worki out the transfer function of the block. Whats confusing me is the input of O2 input of 50. If that wasn't there I know the transfer function would be Oo/Oi=G/1+GH. Homework EquationsThe Attempt at a Solution

Let, we want to calculate the P.E(potential energy) of a system containing 3particles p1,p2,p3.the point of observation is P.so now we should add up the P.E at P due to p1,p2,p3 to get the net potential energy of the system,but why we take the P.E of particles due to each other into count...

If I have a tank half-filled with low boiling point liquid at ambient temperature, then this tank is placed inside dry oven whose temperature is kept to be around 5℃ above the liquid boiling temperature. A fan is placed inside the dry oven as an effort to make temperature distribution even or at...

Homework Statement Homework Equations and the attempt at a solution[/B] Approach: Use the solution for the damped oscillating system provided in the formula sheet. We must use the given initial conditions to find the unknown phase ##\phi## and that will give us an expression for ##x## in...

Homework Statement Give an example of a non-linear discrete-time system of the form x1(k + 1) = f1(x1(k), x2(k)) x2(k + 1) = f2(x1(k), x2(k)) With precisely four singular points, two of which are unstable, and two other singular points which are asymptotically stable. Homework Equations J =...

Find x, y, z solving all the three equations: y^2 + (y*x) - z - x = 0z^2 + (z*y) - x - y = 0x^2 + (x*z) - y - z = 0I would be very grateful!

I'm having trouble understanding the forces involved when defining the equation of motion for this particular problem. So... I've seen the answer for the eq. of motion worked two different ways. The first way involves combining the spring series into Keq = K1⋅K2/(K1+K2). The answer, plugging...

I'm a former physics student and I've been thinking about an interesting problem that eventually led me to the following thought experiment that I'm having trouble resolving. Imagine a two-compartment system, where one compartment is filled with He gas, and the other is filled with standard...

Homework Statement [/B] ##m=3kg## ##M=2kg## Coefficient of static friction between m and M ##\mu_1 = 0.6## Coefficient of static friction between M and the ground ##\mu_2 = 0.8##. The rope is weightless, does not stretch, and the wheel is frictionless. What is the maximum force ##F## that...

Homework Statement Determine the parameters of the PI controller such that two of the closed-loop poles of the transfer function Gclr(s) correspond to the poles of a second order LTI system with the following specifications: i) overshoot S% = 25%; and ii) settling time ts(5%) = 120 s. Homework...

Homework Statement 2. Relevant equationThe Attempt at a Solution ...[/B] Part c) I'm confused as to how the actual pulley system works. If its balanced wouldn't it be stationary. How does it move? I thought that since its balanced the acceleration of the system is constant and therefore to...

Homework Statement A mass m1 is located on a platform with mass M. The platfrom is located on springs with total constant k such that it can swing vertically in direction x. a) Write down the equations of motion assuming mass m1 will always be connected to the platform. Write it as x(t) b)...

Homework Statement This is Rankine-Hugoniot conditions at a hydrodynamic shock front. Where P2=0 v2=0. The problem is attached. I need to solve a system of equations. I thought it would be relatively straight forward solving for the three unknowns but I'm struggling. I know it's possible to...

Hi all, I was working on a problem using Euler-Lagrange equations, and I started wondering about the total and partial derivatives. After some fiddling around in equations, I feel like I have confused myself a bit. I'm not a mathematician by training, so there must exist some terminology which...

First time in this forum, so greetings to everyone! I am currently working with some physical models in the field of natural ventilation and I came across the following 5th order polynomial equation (quintic function): $X^{5}+ C X - C =0$ This is the steady state solution of a physical system...

I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation...