Systems Definition and 1000 Threads

We all know the ##\vec{i}##,##\vec{j}##,##\vec{k}## unit vectors for Cartesian space. But I've never been shown basis unit vectors in other coordinate systems. Do basis vectors exist in other coordinate systems? And if so what are they?

About two weeks ago, I wanted to find out more about the design of lightning protection systems. In particular, I wanted to figure out what gage of wire would be necessary for linking a lightning rod to earth-ground. What I had learned is that the gage of the wire would have to be extremely...

With regards to cellular radio systems1. how many bits of information does each cycle of a sinewave carry on a minimum channel? modulator characteristics 2. A system has narrowband fm characteristics.. name me a rule which is an approximate technique to find the necessary freqeuncy deviation...

Given two systems, Ax=b and Cy=d, for nxn matrices A and C, and n-dimensional vectors b and d, each of which has at least one solution, it is know that one solution is common to both (satisfies both equations). Could such solution be z found by solving Az+Cz=b+d? I understand that a common...

Hello Physics Forums! I need a bit of help. I'm aware that this is not a HW thread, but your help is greatly needed. This could be posed as a general discussion question if this is of any concern. An assignment requires that I have to do research of several contemporary issues in ISE...

1. Homework Statement [/b] A barber shop has two chairs to cut hair and 10 people per hour enter the barbershop to get a haircut. . The average time it takes to get a haircut is 6 minutes. On this particular day, only one barber is cutting hair. Customers that enter the barber shop and use the...

Homework Statement y(t) = ∫∞-∞x(λ) dλ AND y(t) = ∫t-∞x(5λ) dλ Homework Equations The Attempt at a Solution They're both non-causal right? because in the first one the input can be less than t and in the second one it IS less than t? Thanks

Homework Statement How do I know that vector is invariant to changes of coordinate systems if i only have the components of the vector and not the basis vectors? Homework Equations let the vector in reference frame 1 be ds and the same vector in the reference frame 2 be ds1 The...

Something doesn't seem right in regards to my analysis of the Jacobian. What about when $a=0$ at the second fixed point? \begin{alignat*}{3} x' & = & y - ax\\ y' & = & -y + \frac{x}{1 + x} \end{alignat*} First, we need to determine the fixed points in the system. So let \begin{alignat*}{3} y -...

Hello all, I was wondering if there was a way of solving a matrix on a TI-36X Pro that has complex numbers in it. Every time I try, it just says "invalid data type". Is there any way of getting around this? Thanks! Robert

Homework Statement Here is the question from my book along with their solution to the problem : Part 1 : http://gyazo.com/6467751155edcefec6cc583d164d2ae7 Part 2 : http://gyazo.com/d91752f0a18a72af96f6afc74117f011 Part 3 : http://gyazo.com/7a17dbca3e414d0ddc8458abce2eda9c Homework Equations...

Suppose there's a system with given uncertain parameters. And I would like to obtain certain Rise time, max. over shoot, settling time by adjusting those parameters. Let's say this is the second order system; T(s) = (ks + c) / (s2 + as + b) First of all; for a second order system there...

Hi there, I am looking for books that treat signals and systems from a mathematical perspective. When I say "signals and systems", I am referring to the typical second/third year material taught in EE programs: system characteristics (causality, memory, stability), LTI systems, linearization...

I have an electromagnetic field with a Poynting vector that has the following form in spherical coordinates: $$\bar{P}(R,\phi,\theta)=\frac{f(\phi,\theta)}{R^2}\bar{e}_{r}$$ The exact nature of f(\phi,\theta) is not known. Suppose I measure the flux of this vector field by a flat area...

hello all, i need some help on this one. i want to do an article about the posible aplications of quantum entanglement in aircraft flight control systems. i want to entangle two transistors, put one of them at the ACE - actuator control electronics (probably) in the pilot's cabin and the other...

Hi, physics undergraduate here. I don't know much about differential geometry yet, but I'm curious about this idea: Say I encounter a boundary value problem, and I'm not sure what coordinate system would be 'easiest' to solve the problem in. Is there some way to put the differential...

Hello everyone. I'm looking through an old book on optics and something there has me really confused. I attached the two pages I'm referring to, or you can find them here: http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Rays/ as pages 14 and 15 in the pdf. Basically, what's going on is...

Common extensive quatities such as mass, charge, volume can be defined for general systems. I can imagine that we can measure and define them without any problem in case of any kind of complex system as well. However, I do not know the general definition of the entropy, only the thermodynamic...

Good evening, I am currently trying to use Mathematica to find the symbolic solutions to a set of complex linear equations. I have never used Mathematica for such a task before and am finding it quite difficult. Let me state the problem...

How does Matlab or computer algebra systems find derivatives of functions? Is it correct that they use matrix transformation?

Hi guys I have 5 term which each term includes three function of time (autonomous system ), i want to obtain time derivative of each term as other terms for example if i define each term as a dimensionless variable , e.g. x , y , z , v , w , i want to know dx/dt = as a combination of x , y ...

Prove that if \(P\) is a stochastic matrix whose entries are all greater than or equal to \(\rho\), then the entries of \(P^{2}\) are greater than or equal to \(\rho\).

I've been reading a bit about systems science/theory and I understand that in some fields it sometimes pays off to look at how the whole systems behave as opposed to how the individual parts that comprise the systems work. However, there seems to be a certain aspect of systems theory known as...

If I am not mistaken the Bohr model had 3 main problems: the assumption that the electron moves in fixed orbits, the angular momentum assumption's violation of the Heisenberg uncertainty principle, and finally the restriction of the validity of the model for only 1-electron systems ( i.e...

hey, could you help me with a few examples of Underdamped and Over damped systems?

Hi all. I am very puzzled by the following. Let x_1 and x_2 be two coordinate systems related by x_1=1-x_2. Now if y(x_1) = x_1 and z(x_2) = 1-x_2, then clearly y(x_1)=z(x_2). Now integrating the function in each coordinate system gives Y(x_1) = \int y(x_1) dx_1 = \int x_1 dx_1 =...

Homework Statement http://i.imgur.com/j8JdV.png Homework Equations http://i.imgur.com/Wobmo.png The Attempt at a Solution I wasn't really sure where to start with. Can energy level be calculated at any of these, since the signal stretches to infinity? I'm very thankful for any...

After receving $249.1 million grant from the US Department of Energy and $125 million in tax credits and incentives from the Michigan Economic Development Corp., A123 Systems is filing for Chapter 11. What remains to be seen is how the debtors will run the company and if the jobs promised here...

Complex systems is somewhat of a newer/emerging field. I can't do a good job characterizing it, but it is quite interdisciplinary and relies on heavy mathematical and computational modelling of various... well, systems that are complex. (Anything from ecosystems, to stock markets, to weather)...

Hey! I'm having some problems with this question: An electric winch is used to raise a 40-kg package and a 10-kg package vertically up the side of a building as pictured in the diagram. The magnitude of the frictional force acting between the wall and the 40-kg package is 60N. The angle the...

Homework Statement I am given the transfer function Gp (s) = 1/(s+16) and I have to design a controller of the form Gc (s) = K(1 + 1/T*s) (which is a PID controller) To meet the following requirements: Maximum steady state error to a steadily changing desired position = 5% Maximum...

Homework Statement In a Hilbert System, prove: \phi[x|m] \rightarrow\forall y((y=m)\rightarrow\phi[x|y]) where \phi is a formula, y, x are variables and m is a constant. \phi[a|b] denotes the formula obtained by substituting b for a in \phi This problem crops up in my attempting to prove...

In the figure below, M2 has more mass than M1 and M1 has more mass than M3. The questions refer to the magnitudes of tensions and weights. There is friction between the horizontal plane and M2 (mu_k not equal to 0). M2 is observed to travel at a constant speed. Assume that the pulleys are...

Homework Statement A crate is pulled up using frictionless pulleys in the manner shown in the figure. The angle is 45 degrees. The masses are, for the small pulley, m1=3.5 kg, for the traveling pulley, M2=6.5 kg, and for the crate, MC=44.2 kg. What is the minimum tension with which the...

A certain part of a closed loop cooling water systmem has to have some of the pipes made to have a larger diameter to allow more flow. Does this mean though that the overall pressure in the system will drop? I know the headloss in the widened pipe will decrease and flow increase. But will you...

I have this problem in my book: Ann had 20(Cash) less than Betty. Ann spent 3/4 of her money, while Betty spent 4/5 of hers. Then Ann's remainder was 5/6 of Betty's remainder. If Ann had x(Cash) originally, form an equation in x and solve it. And this solution in the answer key: x=Ann's...

For systems under an energy constraint (a conserved Hamiltonian that is a function of the q's and p's in generalized coordinates), is it possible for it to behave chaotically (chaos by its dynamical definition), or will it always have some equilibrium it tends towards?

I'm trying to solve a system of five nonlinear equations (degree 7) in Mathematica: Solve[{q (a^2 + b^2 (3 q^2 + r^2 + 8 t^2)) ((e - q)^2 - R^2 - 4 T^2)^2 + q ((e - q)^2 + R^2 + 4 T^2) - 2 (e - q) (r R + 4 t T) == 0, R (a^2 + b^2 (3 R^2 + (e - q)^2 + 8 T^2)) ((e - q)^2 -...

The Egyptians were known for using base 6 while base 10 is more popular presumably because of the number of fingers we have. How much does the value of the base number of a mathematical system affect the underlying math used to describe physics? Would we still be able to arrive at the same...

Rajah earns an hourly wage plus tips. One week he worked 12 h and made a total of \$117. The next week he worked 10 h and earned the same amount in tips as the week before, for a total of \$110. What is Rajah's hourly wage? I need help getting the two equations

Sabrina has two part time jobs delivering flyers. She earns \$9/h at her weekday job and \$12/h at her weekend job. Last week s he worked 23h and earned a total of \$231. How many hours did she work at each job?

Rajah earns an hourly wage plus tips. One week he worked 12 h and made a total of \$117. The next week he worked 10 h and earned the same amount in tips as the week before, for a total of \$110. What is Rajah's hourly wage?

Provincial Express charges \$4, plus \$1.50/kg, to deliver a package overnight. The Package people charges \$5, plus \$1/kg. When is Provincial Express less expensive to use?

Sook-Lee wants to rent a car for a day so she can visit her sister at university. She has called two car rental agencies. Rent-a-Heap charges \$50 per day, plus \$0.12/km. Kurt's Rent-a-Car charges \$40 per day, plus \$0.20/km. At what distance will the cost of renting of a car be the same from...

Hello forum, why does a system of linear equations really have no solution or one unique solution, or infinite solutions? What forbids a system to a finite number of solutions? thanks fisico30

I have had similar questions posted, but I am not quite sure on this one and it seems that my textbooks have trouble agreeing completely aswell. As far as I understand it: Hamiltons principle: δI = δ∫Ldt = 0 is only satisfied for systems, where the generalized forces can be put in a...

I have narrowed down a control systems question I am doing to the following function in the S-domain.. numerator = (5s+1) denominator = (s+3)(3s+2)(s^2) Using partial fraction expansion - I compute A = 14/63... D = 1/6... B = -2.25 And I can go no further - because both MATLAB and MAPLE...

1. how do i solve X'(t)=A(t)X(t) Homework Equations I know of this equation: x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right) but i think that I'm using it wrong. The Attempt at a Solution i have the following mathematica code: A= x = MatrixExp[Integrate[A, {t, 0, s}]].{1, 0,0,0}...

Homework Statement Determine if b is a linear combination of a1, a2, and a3. a1= [1,-2, 0] a2 = [0, 1, 2] a3 = [5, -6 8] b= [2, -1, 6] The Attempt at a Solution Alright, well I used an augmented matrix to solve the problem, and after reducing it completely, the matrix looked...

Homework Statement Consider the electrical circuit shown: http://imageshack.us/a/img525/8163/p1circuit.png Let the state variables be x1(t)=Vc(t), x2(t)=iL(t), and x3(t)=Vc(t); output is Vo(t). Write the state-space equations in matrix form and find the transfer function, T(s)=Vo(s)/Vi(s)...