Stability Definition and 478 Threads

Hi everyone. I'm kind of new here, please be nice. So I was reading up some physics and came across the fact that if the no. of neutrons is too high compared to the no. of protons, the nucleus becomes unstable. I can understand why this happens with protons, due to the coloumbic repulsion...

a system is said to be stable if its impulse response approaches zero for sufficiently large time. why? please give me an satisfying answer..

For this problem I have taken laplace(one-sided) transform of h(t) which gives me H(s)=1/(s-α). From this I can state that α must be -ve for G(s) to be stable. But my problem is while taking one-sided Laplace Transform the exp(βt)u(-t) part gives 0. So in H(s) according to my calculation, β...

Hello, I am looking for research results, report etc. dealing with -aerodynamic efficiency and static longitudinal stability- Couldn´t find anything useful yet! Any ideas would be very much appreciated. Best Regards, granby

I was assigned a multistep task by my professor so I first made the molecule with ChemDraw, then I ran an optimisation using B3LYP/6-31G. I then ran a frequency scan and checked for any imaginary frequencies. There were no negative frequencies and my understanding is that this means that...

If I place a bicycle wheel on the floor, it flips over and falls down... Same is with the toy top. But when the wheel or the top spin, they remain stable. Can someone please explain the physics behind this?

I've just started a course on organic chemistry and the professor said some things which did'nt exactly make sense to me: 1) In a period, atoms are more electronegative as we go to the right. The more electronegative an atom is, the more stable it becomes. 2) In a group, atoms increase...

We have to determine in which of the following options, the first ion is more stable than the second. 1. 2. 3. 4. 5. 6. Attempt at the question 1. Since in the first one, +ve charge is due to bonding, not deficiency of electrons. 2. First one can get lone pair from N. 3. N...

Homework Statement Two sticks 1 and 2 are attached together at the point B and the stick 1 is placed on point A and all these sticks can be rotated with no friction. If the stick 2 rotated freely around point B, in which direction the stick 2 will rotate? Homework Equations I°ω°=Iω...

I admit I am a bit out of practice when it comes to DiffEq. I think I am either forgetting a simple step or getting my methods mixed up. Homework Statement The problem concerns a pendulum defined by d2θ/dt2 + (c/mL)(dθ/dt) + (g/L)sinθ = 0 where m=1, L=1, c=0.5, and of course g=9.8 After...

x'=y-x^3 and y'=-x^5 I've worked the jacobian which is [-3x^2 1;-5x^4 0] and the equilibrium is at (0,0) so jac = [0 1;0 0] and eigenvalues are both 0 so is the stability non isolated point? and what i can say about the basin of attraction of the origin? Could anyone help me...

I have heard much about how careers in aerospace engineering and astrophysics can be hard to find, one has to move around a lot, and the salary is not great. As far as money goes I don't care too much, but I'd like to make at least 75k a year, but I don't want to have to move around more than 2...

Why do U and Th (and Pu) have so long half lives in comparison with the lighter elements following Bi (i.e. Po, Ra, Rn, Fr, At ..)?

Homework Statement Basically I found the following system of DE's: \frac{dx}{dt}=y \frac{dy}{dt}=-\frac{g}{l} \sin x - \frac{cy}{ml}. (Damped pendulum) I'm asked to analize the stability of the critical points x=0, y=0 and x=\pi, y=0. Using intuition the first point is asymptotically stable...

Hello! I'm doing a modal analysis and I'm trying to extract modal parameters from my aqcuired data. I'm using the Pulse Reflex Software. I got to the point where the Software provides me with a MIF and a stability diagram and I am to choose the parameters. However, I am unsure how...

https://dl.dropbox.com/u/73421703/b1.jpg hi there , I'm asking for help with this one! I should solve that problam through energy method. Given single force Q(not shown in the picture) on the edge of the cantilever(the right-end of the beam), what I'm looking for - The critical P(axial force)...

Basically I'm tying to work on a project that requires a heavy battery mounted on top of a foam floater. i believe that as long as the centre of gravity of the battery and the centre of buoyancy of the foam is close to each other, they will be stable in water or while floating on water. Correct...

In my book, it's written that the phenyl cation can't be stabilized by resonance. I can't think of any reason why this is so. All the conditions for resonance are satisfied : all carbon atoms lie in one plane, all possible canonical structures will have the same number of unpaired electrons...

This is just a simple conceptual question. When we try to calculate a nuclear binding energy of some nucleus, we get the mass defect(del M) and find the binding energy by using (del M)c^2 right? Well, what I do not understand is this. For instance, let's take a formation of a...

So I saw a video on youtube: http://youtu.be/uhS8K4gFu4s And so I thought I'd try to understand the whole stable orbit thing. So first you have a simple energy equation of E = K + U. K = (1/2)mv^2 (kinetic energy) U = -GMm/r^2 (gravitational energy) r = radius of orbit v = velocity of...

I often hear that for planet to have life on it it must have proportionaly large moon to keep it's axial tilt small like Earth is between 21.5° to 24.5° and not like Mars that varies from 15° to 35° which makes destructive effect on possible life that could flourish. But doesn't Venus have...

Hi all Suppose for a dynamical system \dot x=f(x) , x \in \mathbb R^n there exists finite number of isolated equilibria, each of which is locally stable (i.e eigenvalues of the associated Jacobian have negative real parts). My question is: Can this happen for more than one equilibrium...

As we all know, the nuclear stability graph strays away from the y=x line from mass no. = 20 onwards. Why is that?

Hi i am not goin goin going to lie Fluid Mechanics is not my strongest subject. Im struggling to calculate the Metacentric height. Ive got the following: Total weight of assembly (W) = 2.447kgf Ajustible weight (w) = 0.204kgf Breadth of pontoon (L) = 360mm Height of metacentre...

Let's say I have the following transfer function: G(s)=\frac { s-1 }{ { s }^{ 4 }+2{ s }^{ 3 }+{ 3 }s^{ 2 }+{ 4s }+5 } Which is run through MATLAB to obtain the pole-zero format: G(s)=\frac { s-1 }{ ({ s }^{ 2 }+2.576s+2.394)({ s }^{ 2 }-0.5756s+2.088) } Using a quadratic solver...

Does anyone know the theory behind rotational stability of a (long, thin) axle? I would like to know the maximum allowable rotational speed of a 5 meter long axle. I suppose its something in line with the theory of column stability, but I can't find anything about it. I have made a FEM...

Of all the baryons, why are protons the only known stable combination of quarks? Why are neutrons more stable by more than billions of times longer than the rest of the unstable baryons? If it is just their combination of quantum numbers, then, why do those combinations work out to being stable?

Hi, I'm new to posting questions on forums, so I apologise if the problem is poorly described. My problem is solving a simulation of the state of a mineral processing froth flotation plant. In the form x@i+1 = f(x@i), f represents the flotation plant. f is a computationally intensive solution...

Homework Statement Find the equilibrium and determine its stability for the model of Sec 1.4. Assume x and y are both strictly positive (nonzero). Homework Equations Differential equations of section 1.4 (1/x)(dx/dt) = a1 - b1y (1/y)(dy/dt) = -a2 + b2x The Attempt at a Solution I solved...

There is an equilibrium between the conformer in which OH is axial and the conformer in which OH is equatorial. axial - equatorial in apolar solvents, the equilibrium is less displaced to the right than in polar solvents. Any ideas? I think it has to do with entropy but not sure how...

I need help on how to cascade two or three Jfet transistor and the calculation of the values to have a good amount of gain. The cascade also should help in providing good linearity, have less distortion and should stable good stability.Thanks, good help will really be appreciated by me.

An ionic compound is more thermally stable when the metal cation is more reactive. So its harder to decompose. But then what's the difference between melting and decomposition? Also, when an compound is harder to decompose, does it mean its melting point is higher? Because even though Na2O...

If I may, I would like to give this question another try, especially if guys with some cabala in QFT can address it. Is it possible to show in the relativistic quantum theory, that the hydrogen atom is stable? (Electron will not fall onto the proton)? I explain. In the non-relativistic...

Dear friends, I want to find the conditions of stability of a fixed point. consider the function "f" iterates to obtain fixed point "a": x_{n+1}= f(x_n) for this dynamic system, the fixed point "a" is stable if we have: |f ^{\prime}(a)| < 1 Currently I'm working on a bit different...

Homework Statement Consider the transfer function H(s)=\cfrac{1}{a_{2}s^{2}+a_{1}s+a_{0}} where real-valued coefficients a_{2},a_{1}, a_{0} are arbitrary except that a_{2} is nonzero. Verify that the system is stable iff the coefficients a_{2},a_{1}, a_{0} have the same sign. Homework...

Hi, I am trying to find out if a system is bounded (stable) or not, and I don't understand the process, I basically have these two functions, y1[n]=n2*x[n] y2[n]=x4[n] According to my notes, y1[n] is not stable, as the output is proportional to n2 which is not bounded, I understand...

Homework Statement Find the stationary solution(s) of the following system of DE and determine its stability: x'=x-x^3-xy^2. y'=2y-y^5-x^4y.Homework Equations x'=0, y'=0. Expansion of x and y around the critical point: x=x_0+\alpha, y=y_0+\beta.The Attempt at a Solution I solved x'=y'=0, this...

Homework Statement Find the stationary solution(s) of the following system of DE and determine its stability: x'=x^2+y^2+1. y'=2xy.Homework Equations x'=\frac{dx}{dt}=0, y'=\frac{dy}{dt}=0.The Attempt at a Solution I tried to google "stationary solutions of a system of DE" but didn't find...

So I get that conservation of angular momentum makes a spinning top stable. Same mechanism behind gyroscopes. When you first spin a top, there's a lot of wobble (precession), but it quickly dissipates. Why does this happen? The lack of wobbling must be a lower energy state if it is reached...

Hi, I am trying to understand and analyze JK flip flop's (using RS flop flop i.e. using NOR gates). I have written out the characteristic table and when I give Q = 1, J=1 and K = 0 I am trying to analyze the Q' (Q complement) by giving the intial state to 0. I find that Q settles to 1 (i.e...

For the system \dot{x}=y2 \dot{y}=x2 Both the eigenvalues are zero. How do I find the eigenvectors so that I can sketch the phase portrait and how do I classify the stability of the fixed point (0,0)?

confused!..system stability and linearity 1)-Is y(n)=cos{x(n)} a stable system?? and is the condition s=Ʃ|h(k)|<∞ for stability valid only for LTI systems? actually my book solves the given problem using the above method..but according to me the given system is not LTI SINCE ZERO I/P...

I have two satellites flying in formation geverned by the equations of motion including J2 and drag. Now, one of the satellites has more drag than the other so they become appart. I designed a controller (proportional integral) which meassures the along track position between them and gives...

Homework Statement http://imageshack.us/photo/my-images/535/newpicture3.jpg/ Homework Equations Honestly i used the equation in Strogatz 10.3.3 so I am not sure how to do it for others. The Attempt at a Solution http://imageshack.us/photo/my-images/406/worke.png/...

Are particles that are not stable (for example top, bottom quarks; W and Z) when produced in particle colliders possibly stable at very high energies? Are third generation particles stable at high energies? Thanks, Mark

http://en.wikipedia.org/wiki/Gyro_Monorail#Principles_of_operation It appears that counter-rotating gyros can indeed provide stability without precession. Is this simply because of the fact that when you accelerate the rotation of the axis of adjacent counter-rotating spinning wheels you are...

Hi, Explain in terms of the number of nucleons and the forces between them, why argon-36 is stable and argon-39 is radioactive. My first doubt regards the number of nucleons. If a nucleon is the collective number of neutrons and protons, if we take carbon 12 for example, does it have 6 or...

Homework Statement Find the equilibrium points and their stability in the system xdot = xy - 2y - x + 2 ydot = xy + x Homework Equations Jacobian matrix = g'(x) The Attempt at a Solution first find the points that a critical point would satisfy...

Homework Statement y'=(1-y)(3-y)(5-t) Homework Equations find equilibrium solutions of ODE and determine their stability The Attempt at a Solution equilibrium solutions are y = 1 and y = 3, I'm not sure how to determine their stability without some form of a slope field, is it...

Hi, As shown in the attachment, the different situations that occur in an object with 1. the CG above the Centre of buoyancy (CB) and 2. CG below the CB are shown. A. It is said that the more stable state is when CG is below CB...however, I don't understand this point, since as seen in...