Periodic Definition and 437 Threads

Hey all, I want to prove that a function is periodic using the formula: x(t) = x(t+T) where T is the supposed period.An example equation would be: x(t) = 7sin(3t) I would set up the equation like so: 7sin(3t) = 7sin(3*(t+T)) assuming that they equal each other: 3*t = 3*(t+T) solving for...

Homework Statement The question says to solve the Schrodinger equation for a particle in a box with periodic conditions and then it gives. ψ(0)=ψ(a) The Attempt at a Solution I used the above BC and I also did it as its derivative. (It wasn't stated but I assumed it was implied. I had no...

For the scalar linear ODE with periodic coefficients, $$ x' = a(t)x,\quad\quad a(t + T) = a(t), $$ show that the solution is of the form $$ x(t) = x_0e^{\mu t}p(t), $$ where $\mu$ and $x_0$ are constants, and $p(t)$ is a $T$-periodic function. How can I show the solution is of the form...

periodicty -- Sampling of a periodic signal... I have a doubt..is a signal which is sampled from a periodic signal also periodic?if so then is there a relation beyween the time period of the two?

Hello , i am trying to implement this algorithm for 2d grid. 1) i am not sure if my calculations are correct. 2 ) i don't understand how to return my final calculation ( how will i insert to the matrix i want (the 's' in this example) the new coordinates (xup,xdow,yup,ydown)). I mean ...

So Arsenic is poisonous to Oxygen based life forms (Humans). What would be poisonous to a Sulfur based life form (if they exsisted)?

Are there other comets like hally (periodic phenomena's?)

Hi PF, I'm trying to come to grips with the work of Alexei Kitaev on applying notions from (topological) K-theory to the task of classifying phases of topological insulators and superconductors (paper here: http://arxiv.org/pdf/0901.2686v2.pdf). Despite having plenty of citations, I've yet to...

Homework Statement A spring hanging from a lab stand has an equilibrium position of 66mm. Weights are added in 50g increments from 100g upto 250g, record the spring displacement and work out the spring constant. Part 2: With each mass in turn pull them down 20mm from their equilibrium...

Homework Statement Consider a spring hung vertically from the ceiling. a) When a 2kg mass is attached to the spring, the spring is stretched 0.10m. What is the force constant of the spring? b) The 2kg mass is removed and a different one attached to the spring. It then undergoes simple...

ıf the function f :R->R is cont. and periodic with a period T>0 then Are integral from nT and zero f(x) dx and n(integral from T to zero f(x)dx are egual to each other ? I proved by giving examle that it is true. I thinl it is not right way How can ı prove this? Regards

Hi, I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model. I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N? I.e...

Let $f:\mathbb R\to\mathbb R$ be a continuous function of period $2\pi.$ Prove that if $\displaystyle\int_0^{2\pi}f(x)\cos(nx)\,dx=0$ for $n=0,1,\ldots$ and $\displaystyle\int_0^{2\pi}f(x)\sin(nx)\,dx=0$ for $n=1,2,\ldots,$ then $f(x)=0$ for all $x\in\mathbb R.$ I know this has to do with the...

I have the following ODE system \begin{cases} x' = v \\ v' = v - \frac{v^3}{3} - x \\ x(0) = x_0 \\ v(0) = 0 \end{cases} I am asked to find x_0>0 such that the solution (x(t),v(t)) is periodic. Also, I need to find the period T of such solution. I don't know how to solve the...

user meopemuk mentioned this: In the case of a crystal model with periodic boundary conditions, basis translation vectors e1 and e2 are very large (presumably infinite), which means that basis vectors of the reciprocal lattice k1 and k2 are very small, so the distribution of k-points is very...

Hi everyone! I've written a M-file to draw a sawtooth periodic function as below: function y = sawtooth_w(x) % We find the period number of every element % in the input vector p = 1; %k = 4; tn = ceil((x+p)/(2*p)); % and we subtract that corresponding period from % the base value...

I'm taking a signals and systems class and the textbook (Signals and systems by Oppenheim) says the CT complex exponential of the form x(t) = C eat with C and a complex is a periodic signal. I fail to see how. Let C = |C| ejα (exponential form of a complex number) and a = r + jω (rectangular...

Hello.It seems that older periodic tables showed just eight groups but most modern periodic tables now show eighteen.Are there any reasons why eight used to be preferred and why eighteen is now chosen?I'm guessing that the change over is due to...well I don't know.Thanks for any answers.

Any opinions would be appreciated.

Hi all, In a periodic array of ions, e.g. a metal crystal, the conduction electrons are free to move around. I have read that distortions to the periodic array can cause a decrease in conductivity of the crystal. These can be crystal impurities, phonons etc. My question is, why should the...

Homework Statement http://imageshack.us/photo/my-images/824/50177563.png/ I need to find the Fourier coefficients and estimate the series for certain values of n. (4, 20 and 100) Homework Equations http://imageshack.us/photo/my-images/839/32591148.png/ The Attempt at a Solution...

Homework Statement Discuss the evidence from the periodic table of the need for a fourth quantum number. How would the properties of He differ if there were only three quantum numbers, n, l, and m? Homework Equations The Attempt at a Solution The Pauli Exclusion Principle...

Homework Statement f(t) defined by f(t) = |t| for (-pi,pi) and f(t+2pi)=f(t) the graph is just ^^^ where w=2pi/T = 1 Homework Equations Periodic function using Trigonometric from Even Function f(t) = (1/2)anot + (the sum from n=1 to inf) (an)*COS(nwt), where an = 4/T Integrated from 0 to...

Hi, On a surface evanescent waves are created when total internal reflection occurs. However when this surface has periodic structures of appropriate periodicity (gratings, photonic crystals) the evanescent waves are "freed" from the surface and they propagate to the surrounding media. I am...

Hi, On a surface evanescent waves are created when total internal reflection occurs. However when this surface has periodic structures of appropriate periodicity (gratings, photonic crystals) the evanescent waves are "freed" from the surface and they propagate to the surrounding media. I am...

Homework Statement Hi, my question is whether the sum and multiplication of two periodic functions (with a common period) are periodic. Our functions are R\rightarrowR. Homework Equations The Attempt at a Solution f(x)=f(x+T) g(x)=g(x+T) T is the period. h(x)=f(x)+g(x)...

Hello everybody, I was wondering whether someone has more information on the influence of inconsistant initial conditions on solving a system of ODE's with periodic solutions using a time marching method like a 4th order Runge-Kutta scheme. The phenomenon I am studying is described by a...

Hi, I solved a steady state problem involving a bar fixed to string in the left side and pulled periodically on the right side f(x,t)=P_0sin(wt). To check the solution i made E (young's modulus) go to infinity, essentially making the bar rigid. the expression i expected to receive is: u(x,t) =...

Homework Statement A function f(x) has periodic derivative. In other words, f'(x +p) = f'(x) for some real value of p. Is f(x) necessarily periodic? Prove or give a counterexample. I believe it is true simply because of trigonometric functions. However, I do not know how to prove it. I...

Homework Statement A function f(x) has a periodic derivative. In other words f ' (x + p) = f ' (x) for some real value of p. Is f(x) necessarily periodic? Prove or give a counterexample. Homework Equations Periodic functions and Periodic Derivatives The Attempt at a Solution To be...

Im having a little trouble about how to go about defining this signal. It has a sqrt(-1) in it raised to a power so this is where i get confused. No doubt my poor algebra skills may be holding me back from understanding this problem. The signal is x(k)=j^-k u(k) I need to determine: A...

Hi, This is probably trivial, but I don't see it and would therefore appreciate receving inputs. Suppose we define a state |\phi_{lr}\rangle = \sum_{n=0}^{N/r - 1}\sqrt{\frac{r}{N}}|l + n r\rangle How is the quantum Fourier transform of this state equal to...

curvilinear coordinate systems and "periodic" coordinates Hello, we can consider a generic system of curvilinear coordinates in the 2d plane: \rho = \rho(x,y) \tau = \tau(x,y) Sometimes, it can happen that one of the coordinates, say \tau, represents an angle, and so it is "periodic"...

So my question is if I periodically heat some glass of liquid from an arbitrary source, hence providing a driving frequency for the system that will give rise to a phase lag between the temperature of the liquid and the incoming heat from the source, how can I show that there will be a possible...

I'm currently studying grade 11 chemistry... And the periodic table of elements slightly confuses me. I am having trouble understanding which are metalloids, and halogens. In the handout that my teacher gave me, it listed the following as metalloids: B, Si, Ge, As, Sb, Te, Po, and At. It also...

So for my inorganic class we need to know the periodic table by heart, as we will not be getting one on our tests. While memorizing groups and periods in order doesn't hold that much practical sense (it would be much better to be able to just recall any element by it's number along with it's...

what is basic principle followed by atoms to arrange in basic structure?

Is it possible to impose boundary conditions on the other 2d lattices like a rhombic lattice? a hexagonal lattice? an oblique lattice? How does one typically index such lattices?

Is tan|x| periodic and if not, why not? I just found in my book that tan|x| isn't periodic, and how do we make up a rule how to seek periodicity of functions. I.e. ln(sin(x)), e^sin(x)... etc

is it possible to find a function f different from f(x)=constant with the property f(kx)=f(x) for some real and positive 'k' ? this is somehow 'dilation periodicity' is the equivalent to the periodic funciton f(x+k)=f(x) for some positive 'k' for the traslation group

Homework Statement Hello, I am having problem solving this problem (picture below). The figure IS drawn to scale. A = 70 Volts Q1. What is the numerical value of V(2) on the graph (in volts)? Q2. What is the numerical value of point B on the graph (in volts)? Q3. What is the period for...

Homework Statement Prove that the following system has at least one periodic orbit. x' = x - y - 2x3 - 2xy2 + x2sqrt(x2 + y2) y' = x + y - 2x2y - 2y3 + xysqrt(x2 + y2) Homework Equations The Attempt at a Solution I converted to polar coordinates to get r' = (xx'+yy')/r and...

are there non-connstant function that satisfy the following asumptions ?? y(x)=y(kx) they are 'periodic' but under DILATIONS and also satisfy the differential equation of the form (eigenvalue problem) axy'(x)+bx^{2}y''(x)=e_{n}y(x) if the Lie Group is of translations y(x+1)=y(x)...

Homework Statement This is problem 2.4.11 from Thomson, Bruckner, and Bruckner, "Elementary Real Analysis." It is from the "Challenging Problems" section of Chapter 2, Sequences. Note that differentiation and continuity have not been covered at this point, but it is presumed that the reader...

hi , can anybody give me some examples of 'systems of linear differential equations with periodic coefficients'? i don't know how to solve it.. where can i get problems and solutions on this?

Hello, I know I am asking for advice about a very specific topic - periodic functions, almost periodic functions and quasi-periodic functions. I was hit by an idea and I need to know a few things more comprehensively about this topic !?~ :] I am aware that "periodic functions etc." isn't a...

Homework Statement Hi, Have completely forgotten how to prove that a sinusoidal waveform is periodic and can't seem to find it anywhere. So was hoping someone could here. I've got the signal x(t)=cos(2t+pi/4) and am trying to prove it is periodic. Homework Equations wt=theta f(x+k)=f(x)...

This is part of a past paper I am trying to work through before a physics of fluids exam in a month.The angular frequency ω of a periodic surface wave with wavenumber k on deep water is ω = sqrt(gk) where g is the gravitational acceleration. Obtain an expression for the wave’s phase velocity in...

can someone help me determine whether this sequence is periodic? [cos((2pi/3)n + pi/6) + 2sin((pi/4)n)] where n is all integers i know that for a function to be periodic, x(n) = x(n+N) however, i am confused because both the cos and sin component contain n please help. thx.

Specifically on a calculator which makes it hard to determine the period of the function. I realize you're supposed to find the period, and add random X values to that period and see if the Y is the same for both the X + period and just the X, but I have to go over 10 functions and determine...