Periodic Definition and 411 Threads

A periodic function is one that ##f(\theta) = f(\theta + nT)##, by definition. However, the argument ##\theta## can be function of space and time ( ##\theta(x, t)## ), so exist 2 lines of development, one spatial and other temporal: $$f(\theta) = f(kx + \varphi) = f(2 \pi \xi x + \varphi) =...

Hey! :o The Fourier series of $f$ is $$f(x) \sim \frac{a_0}{2}+ \sum_{n=1}^{ \infty} {(a_n \cos{(\frac{2 n \pi x}{L})}+b_n \sin{(\frac{2 n \pi x}{L})})}$$ How do we know that the series of the right part of the above relation is periodic with period $L$?

One period of the function $$f(x)=\operatorname{tg}\frac{11x}{34}+\operatorname{ctg}\frac{13x}{54}$$ is $$918\pi.$$ Please help me to prove that this is the smallest positive period. I can not use the most of trigonometric identities.

Homework Statement Hey, the question i have been given reads: By a simple change of variables, show that if g(x) is a periodic real valued function with period L it can be represented as g(x)~ ∑∞n=-∞ An exp(-2\piinx/L) where the complex constants An are given by LAm =[L/2,-L/2]...

Not a homework problem, just a question. What is a periodic driving force, specifically what is periodic about it? Is it the magnitude of the force that is periodic? Homework Statement Homework Equations The Attempt at a Solution

Can a function have two periods? If so, which is the fundamental period? Consider the following function, $$ f : \mathbb{N} → \mathbb{R} $$, defined by f[n] = 1 if n is a multiple of 2 or 3, and 0 otherwise. Then it is clear that 2 and 3 are both periods of this function, since translation...

So I understand that a surface is triply periodic when the surface is invariant under three tanslations in R^{3}. When looking at the primitive for example, how is that translation defined? Say that the primitive is a set defined by the equation cos(x)+cos(y)+cos(z)=0 My guess is that...

Hey! :o Given the Markov chain $\{X_n, n \geq 1\}$ and the following probability transition matrix: $\begin{pmatrix} 0 & 1/3 & 2/3\\ 1/4 & 3/4 & 0\\ 2/5 & 0 & 3/5 \end{pmatrix}$ All states communicate, so the chain is irreducible, isn't? Could you tell me if the state $2$ is periodic?

Correct me if I'm wrong, but exist 3 forms for represent periodic functions, by sin/cos, by exp and by abs/arg. I know that given an expression like a cos(θ) + b sin(θ), I can to corvert it in A cos(θ - φ) or A sin(θ + ψ) through of the formulas: A² = a² + b² tan(φ) = b/a sin(φ) = b/A...

Hi, last semester I did a project with two fellow students. We made a numerical model to calculate the reflectance from a periodic V-shaped structure of silicon similar to this: In the course of doing so, we came across something we could not explain. I have placed an image of it below...

Homework Statement In "oppgave 4" http://www.math.ntnu.no/emner/TMA4120/2011h/xoppgaver/tma4120-2010h.pdf you have a periodic function which is NOT periodic from ##x=-L=-\pi## to ##x=L=\pi##, but at ##x=0## and ends at ##x=2 \pi=2L##. The formulas I have (like these...

I have a homework problem that I need to use the steady periodic oscillation to solve, so instead of having help on the problem I'd rather just understand how they did it then apply it to my homework (I think that's alright?) I'm kind of wondering where my book gets this from...

Who can provide a physical understanding to this solution to the 3D periodic Navier-Stokes equation: http://purvanced.wordpress.com?

Ashcroft & Mermin, Solid State Physics, page 315: "According to the Bloch theory, an electron in a perfectly periodic arrays of ions experiences no collision at all". But how about the electron at the border of Brillouin zone? How does diffraction take place there?

Homework Statement In the dirac notation, inner product of <f|g> is given by ∫f(x)*g(x) dx. Why is there a 1/∏ attached to each coefficient an, which is simply the inner product of f and that particular basis vector: <cn|f>? Homework Equations The Attempt at a Solution

Homework Statement Number 12. Ignore the scribbling and the circled answers. http://i.minus.com/i17OAHo9PELaW.jpg Homework Equations The periodic table trend of acid/base behavior says that oxides of elements on the right of the periodic table will behave as acids in water. It...

Hello, I have a data set that follows an equation similar to sin(x)+x. Just from eyeballing the data, it seems like there should be a pretty simple trigonometric function A*sin(B*x)+C*x. I went to school for engineering so I have some basic/intermediate knowledge of mathematics but it's...

Homework Statement A 100Ω resistor is connected in series with a 2 uF capacitor and a 20 mH inductor. The voltage 1 sin 5000t + 0.5 sin 1000t V is applied across the circuit. Determine: a) The effective (rms) voltage b) The effective (rms) current c) The true power d) The...

1. Regarding: Transition metals of the Periodic Table 2. Here's my question: the D-Block transition metals will always lose e- (& never gain e-'s) to fully fill (or half-fill) their d-subshells, right? 3. Given what I learned about stable, fully-filled and half-filled subshells...

Hey all, suppose there's a particle with Potential Energy : U(x) = A*[ x^(-2) - x^(-1) ] , where A is a constant. I'm supposed to find the energy required to make the particle go from periodic movement to unlimited movement. First thing I did was U '(x) = 0 to find the balance points, now...

Homework Statement The problem/question is attached in the file called "homework". In the third signal (the peridic rectangular wave), I am requested (sub-question b) to find the Fourier series of the wave. Homework Equations The file called "solution" presents a detailed solution to the...

Homework Statement Could you please help me to start this question? Calculate the properties of complex periodic waves. A 100Ω resistor is connected in series with a 2 uF capacitor and a 20 mH inductor. The voltage 1 sin 5000t+0.5 sin 1000t V is applied across the circuit...

Hi; In chapter 9 of Solid state physics of Ashcroft&Mermin(Electrons in a weak periodic potential), there is a General Approch to the Schrodinger Equation when the Potential is Weak. i can't understand what is meant by the term DEGENERACY? or what does "nearly degenerate free electron...

Hi! I was wondering: is it possible to have a non-orientable surface in 3D which is parametrized by u and v, with u and v periodic (i.e. is it possible to map the torus continuously into a non-orientable surface in 3D?) If so, does anyone have any explicit examples?

Homework Statement The following picture is supposedly periodic (or at least my teacher says so). Could anybody suggest where I begin in order to determine the wave function for this messy graph. Please see the attached for the graph.

\sum_{k=0}^{∞} (t-2k) [u(t-2k)-u(t-2(k+1))] = f(t) where u is the step function and the graph of this is supposed to be 45 degree lines repeating to infinity. Sort of like / / / / / / / / / ad infinitum. I took this equation out of this lecture note on page 10. Fig 5.4 is supposedly the graph...

Homework Statement Is f(x) = cos^2(x) + sin^2(x) a periodic function? Homework Equations sin^2(x) + cos^2(x) = 1 The Attempt at a Solution This question is just something that randomly came to my mind (not a homework problem). I know cos^2(x) and sin^2(x) are both periodic...

Could one always write the periodic potentials in the form: v(r)=Ʃf(r-G) where the sum is over G (reciprocal lattice vectors)?

In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations: x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi). This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...

Compute the power contained in the periodic signal x(t) = 10.0[cos(160.7πt)]^4 The problem I have is I end up with a constant value for ak for all values of k -I start by using inverse Euler formula -Do the appropriate integration -Then consider k for odd and even values My working is...

We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.

I quote an unsolved problem from another forum posted on January 8th, 2013.

Okay so I am solving the SE numerically for different potentials. Amongst those I am trying to find the low energy wave functions for a periodic potential of the form: V=V0cos(x) Now recall that for a numerical solution, at least the type I am doing, you somehow have to assume that the wave...

When a force is applied to a pendulum, the pendulum sways back and forth until it eventually stops. In this problem however, a force is applied at uneven time intervals while the pendulum is still in motion. The force is always applied in the same direction. A data set is given containing...

Homework Statement Hey guys. So I have this homework exercise where I have to convert the following periodic function in radians into a periodic function in time. f(θ) = (80/∏2) θ, -∏/2 ≤ θ ≤ ∏/2 (80/∏) - (80/∏2) θ, ∏/2 ≤ θ ≤ 3∏/2 Homework Equations θ = ω0 t ω0 = 2∏/T...

Homework Statement Consider an LTI system with impulse response h(t) = (0.5sin(2t)/(t) Find system output y(t) if x(t) = cos(t) + sin(3t) Homework Equations y(t) = x(t)*h(t) The Attempt at a Solution I am only familiar with doing much simpler convolutions using graphical...

Homework Statement Is the function cosx + cos(sqrt(2)x) is periodic? Homework Equations cos(x)=cos(x+2pi) The Attempt at a Solution For the above function to be periodic: cosx + cos(sqrt(2)x) = cos(x+T) + cos(sqrt(2)(x + T)) Does that imply that 2pi = T AND 2pi = sqrt(2)T, ergo...

Homework Statement Let f be a 2π-periodic function (can be any periodic really, not only 2π), and let g be a smooth function. Then lim_{n\rightarrow∞}\int^{B}_{A} f(nx)g(x) converges to \frac{1}{2π}\int^{2π}_{0}f(x) The Attempt at a Solution So far, I've come up with somewhat of...

Suppose that $f(\theta)$ is a continuous periodic piecewise differentiable function. Prove that $f(\theta) = f(0) + \int_0^{\theta}g(t)dt$ for a piecewise continuous $g$. I just need a nudge in the right direction here.

Do non periodic signals have frequency? Because my pretty general rule f = 1/T says that they have zero frequency. But suppose i analyze a voice signal. We generally associate a term frequency with them. If you ever had used audacity you might have noticed that the graph is quite...

Why did Mendelev order the elements according to their atomic masses rather than their atomic number? Why did Mendelev not include noble gases in his periodic table?

i don't know how i can use MATLAB to plot anti periodic fun .. the origin site give this code for triangular fun: fs = 10000; t = -1:1/fs:1; x1 = tripuls(t,20e-3); plot(t,x1), xlabel('Time (sec)');ylabel('Amplitude'); title('Triangular Aperiodic Pulse') but when i use this for sine...

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...