Systems Definition and 1000 Threads

Hello, I'm trying to figure out the free body diagrams for the inverted pendulum problem and I'm having trouble figuring out the one equation: ##Psin\theta + Ncos\theta - mgsin\theta = ml\ddot{\theta} + m\ddot{x}cos\theta## I've never really seen a mixed sum of forces equation before where some...

As I understand it a Green's function ##G(x,y)## for a translationally invariant differential equation satisfies $$G(x+a,y+a)=G(x,y)\qquad\Rightarrow\qquad G(x,y)=G(x-y)$$ (where ##a## is an arbitrary constant shift.) My question is, given such a translationally invariant system, how does one...

Godels Incompleteness Theorem states that for any formal system with finitely recursive axioms we can construct a Godel sentence G that is unprovable within that system but is none the less true. Does this still apply to formal systems which, instead of creating Godel numbers for arithmetical...

Homework Statement Starting from rest, two identical boxes are pushed through the same distance. Box A experiences a force F, while box B experience a force 2F. What is true about their final speeds?- The final speed of box A is twice that of box B. - The final speed of box A is equal to that...

Hi everyone, I'm having some trouble understanding how convolutions are applied to systems. Suppose I'm given the impulse response of a system as ##g(t) = u(t)## and I'm also given the system input ##x(t) = u(t) - u(t-2)##. The system output should then be given by: $$y(t) = g(t) * x(t) =...

Hey pf! Learning about macroinvertebrates and their relation to stream systems, and I am trying to understand what stream factors affect their distribution and diversity! I understand that flow rate, and substrate for example have an affect, but why exactly flow rate affects macro's is still a...

Is there a mathematical way to show that a dissipative (or general?) dynamical system obeys the laws of thermodynamics? I am looking for books/sites/references, thanks for any reply.

Homework Statement A specific type of ideal gas has a specific heat capacity at constant pressure (cp=cv+R) that is a function of temperature T, such that cp=0.5+876T, where cp has units of J/kg/K and T has units of K. The gas, which is initially at T1 = 294 K and P1 = 1x105 Pa, undergoes a...

Homework Statement Suppose I've got a static mass on a downward plane. (For instance a car on a drive way). How would you set up this free body diagram? Homework Equations F = f1+f2...etc The Attempt at a Solution My preference is A, but I've seen it displayed in examples in my book as B...

Homework Statement apparently momentum is only sure to be conserved in a closed system - no external forces. So that means if a toy car collides with a wall then the total momentum efter won't be the same as before. That is because the wall would be joined to something else and ultimately to...

Hi everyone, I'm taking a Design of Experiments class which is focused on statistically designed experiments. I'm a bit lost for project ideas and this is my first graduate class. Would anyone have any ideas for an experiment that would have at least controllable factors that might have...

In an operating system, system call is an interface to provide services to the user. Services include I/O operations, process management etc. Further, the C library provides me API above these system calls to make life easier. So printf, scanf internally use these system calls in the end. Q.) Am...

Hello, Is anyone familiar with GIS? I'm thinking about switching for my BS then doing an MS or PHD. Does anyone know how these skills support other fields in the private sector or goverment? Also I want to do something 'sciencey'...so how 'sciencey' is it?

Is it viable to use the law of religion under a secular court? Catholic priests aren't allowed to marry (which is under their religious law), and thus removing his right to marry, for example. So, if the priest were to file a case stating that he was not allowed to marry, is it sensible? Of...

Homework Statement Finding the complete response (steady-state and transient) is a long and laborious task. My lecturer's notes read (since at our stage of the course, we're mostly interested in the steady-state part of the solution and not so much the transient) : "The simple method for...

Homework Statement Hi, When finding the steady-state response to a sinusoidal input, since "s" is a complex number, (a + jw), why do we substitute "s" with only the imaginary part (jw) in the transfer function, G(s) , to get G(jw), rather than substituting the whole complex number to get G(a +...

Hi, I'm having a bit of a problem, and I'm not sure where to put the question. So here's a picture Sorry about the picture, Tank B should really be half-full of water and steam. Ignore the turbine part. I'm trying to create a distillation device and the basic idea I had was to have a boiler...

Hi guys, after hours of searching internet I couldn't find much real-life examples of second order nonlinear dynamic systems (only tons of tons of equation and system theory... got totally frustrated). They will serve as a base process for modeling controllers. So far I found propeller pendulum...

< Mentor Note -- thread moved to HH from the technical engineering forums, so no HH Template is shown >[/color] Hi. Please see question no. 1 in the attachment. If i take the inverse Laplace transform or the Z transform, how can i actually get the value of sampling period 'T'. or is there any...

Homework Statement I have a problem with understanding the thermal circuit I attached to this thread. Please help. It's a Thermal circuit of a computer CPU that needs to be simplified to have just 2 lumped capacitances and resitances. How would one go about doing that? along with the equations?

As the title suggests, I want the tips from the pros. I've learned all of the methods, but going into Calculus/Physics, which methods should I take preference to? Furthermore, will there be significant use of systems of equations in Physics or Calculus in college? P.S.: I know how to graph the...

Homework Statement What is meant by the term tapping in power system , I studied in my textbook that generally from feeders no tapping is taken to the consumers , therefore current loading of feeder remains the same along its length. I was not getting what is being referred here ..?Homework...

I know the debate about Schrodinger's cat is usually about things like consciousness but I want to talk about what it might say about isolated systems. Does the wave function of isolated systems remain in a superposition of observable states no matter how large the system gets? Say you have...

I'm fascinated by the prospect of them, but I can't seem to find much information/progress online aside from like small sensors which aren't quite the same thing. Has there been anything developed that is a self powered vibration generator? As in, it vibrates and then is powered by its own...

There are very results published about PT symmetry breaking in optical systems, with effects like anysotropical transmission resonance in waveguides. But if PT symmetry is broken in a optical system and CPT symmetry must always be respected, then what C symmetry is broken in a optical system?

I want to purchase the Logitech z623 and add to it two creative inspire M2600 speakers (only the speakers, not the sub-woofer). The reason for doing this is because the Logitech system sounds really nice, it has an amazing bass, but mids and highs are not the best and I wish they was as clear as...

Homework Statement Hello, the plot in the image shows a modulated signal s(t), with one period of the modulating signal m(t). The mean value of m(t) is equal to zero . Its asked me to find the modulated index, the amplitude of the carrier, the equation of the message(m(t)) and the kind of...

Homework Statement Find the impulse response for the systems governed by the following equations: 3y(t)'+5y(t)=x(t)+x(t)'[/B]Homework EquationsThe Attempt at a Solution I tried to obtain the homogeneous solution for h(t)[/B] and then I failed to obtain the coefficients of the solution

How controlling a device is possible using wireless communications systems like software defined radio?

I'm trying to create a model which is of the form y = (a0 + a1l)[b0+MΣm=1 bmcos(mx-αm)] [c0 + NΣn=1 cn cos(nz-βn)] In the above system, l,x and z are independent variables and y is the dependent variable. The a, b and c terms are the unknowns. To solve for these unknowns, I have two separate...

Homework Statement I'm trying to derive the equations of motion and state space as well as the transfer function for a system which has two mass spring damper systems stacked on top of each other. The system is base excited. I attached a pic of the system Homework Equations - Sum of the...

Homework Statement Given (135)x + (144)x = (323)x. What is the value of base x? Now we can find out the value of x by simply converting to decimal both the sides , form a quadratic equation and solve but once in a random lecture our prof. taught us a kind of short method to solve this in less...

Homework Statement In Herbert Callen's text 'Thermodynamics and an introduction to thermostatistics', 2nd edition, Problem 1.10-1 on page 32 presents ten potential fundamental equations of thermo systems, labelled (a) - (j), and asks the reader to identify the five that are invalid because they...

At first, good evening. I want you to know that Eng is not my first language, so you could find many errors while reading my posts. I was reading something about qubit and multiple qubit systems, which combined can create a powerful processor for a new type of computer. I'm not sure of how...

The unilateral laplace transform integrates from 0 to infinity.Then how can i take laplace transform of exp(t)u(-t)?PS:I don't want to flip it and use time scaling property.

I have some questions related to how a discrete control system is designed. One method is to design the controller in the continuous time domain, arriving at a transfer function (in the s-domain). After that, a transfer function for the ADC system must be taken into consideration. I will suppose...

Hello, If for a curve in Cartesian coordinates ##||\dot{{\mathbf r}}||=\mbox{const}## (i.e. the curve is constant speed) will the speed of the curve change in cylindrical and spherical coordinates? Could someone experienced share how the transition from flat Euclidian space to curved space...

I have seen a lot of effort go into finding cheap, safe, high energy density phase change materials to store energy in the form of heat so power produced during the daytime may be delivered at night time. But I have an issue with storing energy in phase change materials. They rely on chemicals...

Hi. This might be a stupid question (I'm studying engineering :p), but how do you prove that all numeral systems (binary, ternary etc.) can represent every countable number? I guess you will need to prove that any number ##N## can be written as ##N= S^0 n_0 + S^1 n_1 + S^2 n_2 + ...## where...

Homework Statement A shaft 2 m long rotates at 1500 revs min–1 between bearings as shown in FIGURE 2. The bearings experience forces of 5 kN and 3 kN acting in the same plane as shown. A single mass is to be used to balance the shaft, so that the reactions are zero. The mass is to be placed at...

The equivalence between descriptions of time evolution in QM are rigorously defined and proved for conservative systems as explained for instance among many other sources in Jauch's "Foundations of quantum mechanics" in the chapter 10. However, and an exception is the cited reference, it is not...

Homework Statement Where would be the perfect place to place a fiducial marker in a: mass on a spring system (vertical) and a simple pendulum? Homework EquationsThe Attempt at a Solution My teacher told me that for a simple pendulum it would be below the bob at equillibrium position because...

I've decided that after I finish my MA Math next year I'm going to apply to this program. It's actually a hybrid program that allows people to take classes part time. They do have a modest residency requirement for two consecutive summers, and they're generous in transferring courses. I live in...

Homework Statement 243 is a decimal number. You must convert it to base n, where n will be computed using the digit (d) 5. For example if your digit (d) was "7" , then n is calculated as :n = d % 6 + 2 (where d = 7) = 7%6 + 2 = 3 Homework Equations None. The Attempt at a Solution n = d % 6 +...

Guys Can you help me out, i don't know if I've done this right. Question: 243 is a decimal number. You must convert it to base n, where n will be computed using the digit (d) 5. For example if your digit (d) was "7" , then n is calculated as: n = d % 6 +2(where d=7)=7%6 + 2 = 3My Working: n =...

Hello! :) Here's another problem that I want to fully understand how it was solved. The part that I'm having a hard time with is the taking-derivatives of some equations. Why did the solver decide to take the derivative of equation 2. And why the second derivative of equation 1 became like...

I live in Florida, and I've been looking for a website that will tell me what the sky will look like over my location and what each star is, but I can't find it. Anyone know if anything exists similar to what I'm describing? Thanks.

Homework Statement Hello, I am given the following problem. A balanced three phase 4 wire supply has r.m.s. line voltage of 415V and supplies a star-connected load made of 3 impedances: Za = 10 - j10; Zb = 10 + j10; Zc = 0 + j8; Calculate the current phase and neutral currents, also the total...

I'm told the delay time (the time i turn down the thermostat and the time the AC kicks in) is a safety measure to let the coolant pressure equalize. I don't really understand why.