# Tagged Questions

Questions on periodic functions, functions $f(x)$ that satisfy the identity $f(x+c)=f(x)$, for some nonzero $c$.

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### My brain doesn't work right now: What's the formula for the $n$th vertex of a discretized sine wave?

So far I have: $$A \sin(2\pi f ? + \phi)$$ where $f$ is cycles per second, and $\phi$ is in seconds. If I'd like to approximate the sine wave with $N$ points per cycle, and I want to draw $C$ ...
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### How to find periodicity of a nim sequence?

I am trying to solve a problem which is a simple algorithmic game. Link to the problem - https://community.topcoder.com/stat?c=problem_statement&pm=6856 I have basically figured out that for ...
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### period of the function $y = \sin^2\frac{\sqrt2x+3}{6\pi}$

Today I came across a question The fundamental period of the function $y = \sin^2\frac{\sqrt2x+3}{6\pi}$ is $\lambda \pi^2$ then the value of $\frac{\lambda}{\sqrt2}$ is ___ I tried to equate ...
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### How to prove that the ellipse is a periodic orbit knowing that the orbital derivative of a function V is zero on there

The question is as follows: Show that the orbital derivative of the function $V=(1-x^2-2y^2)^2$ is zero on the ellipse $x^2+2y^2=1$, and explain why you can deduce that the ellipse is a periodic ...
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### Proof: A solution to a periodic ODE shifted by a constant time is another a solution to that ODE.

This is probably a trivial question but I don't have a clue where to begin. Suppose $x(t)$ is a T-periodic solution to the differential equation $$\frac{dX}{dt}=F(X)$$ where F(X) is in $C^1$. Show ...
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### True or False: $f(z)=Ln(z)$ is periodic

From Wolfram MathWorld: A function $f(x)$ is said to be periodic with period $p$ if $f(x)=f(x+np)$ for $n=1,2,3...$ The easy bait here is to realize that $Ln(z)$ is asking for the principal ...
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### Are there any theorems linking periodic functions to the number of times they are differentiable?

I was working through some Fourier series questions and I was wondering if the periodicity of a function has anything to do with the number of times it's differentiable. For instance, the elementary ...
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### Compute Limit Involving Integral and Periodic function [closed]

If $f: \bf R \to \bf R$ is continuous and periodic with period $T$, then show that $$\frac{1}{t}\int_{a}^{a+t}f(s)ds \to \frac {1}{T}\int_{0}^{T}f(s)ds$$ where $a\in \mathbb{R}$ and $t \to \infty$...
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### Periodicity of a trigonometric function

How to find the fundamental period of the function $|\sin x - \cos x|$ and $|\sin x - \cos x|$ + $|\sin x + \cos x|$? Please tell the proper method to find the period of the functions like these. I ...
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### Why is there periodicity in the output of Richard Voss' fractional Brownian motion?

I am trying to figure out why the output of fractional Brownian motion (fBm) as described by Richard Voss (Random fractal forgeries. In: Fundamental Algorithms for Computer Graphics, R. A. Earnshaw (...
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### how to get the solution?

I take the next exercise from Apostol's book. I thought for a while , but nothing. Then I read the solution. I try to think: how did he get it , but nothing. I want to know how to get to the solution. ...
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### Periodic orbits on centre manifold

I am interested in periodic orbits of mechanical systems of second-order dynamics with no damping, i.e. governed by an equation of the type $$(1)\quad \ddot x + f(x)=0$$ ...
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### How to find out the Power of $x(t)$?

I am studying signals and system. I learned that \begin{align} P&=\lim_{L\to\infty} \frac 1{2L} \int_{-L}^{L} |x(t)|^2 dt\\ P&=\frac 1{T} \int_{<T>} |x(t)|^2 dt ~~~\mbox{, P could be ...