# periodic

1. ### Show that function is periodic (Fourier series)

Hi, I have the following problem: Assume that the function f is 2\pi-periodic and has the Fourier series: f(x) = a_0 + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) Let k \in \mathbb{N}. Show that the function g(x) = f(kx) is 2\pi-periodic, too. I am in general quite unsure how to start...
2. ### Digital Signal Processing -- Periodic Signals

Hi, I am stuck on simplifying the following. Iam wondering if anyone could help me fill in the blanks please? x[n] = 1 + sin (πn/4) + 2 cos (πn/2) where sin = {exp(j) - exp(-j)} /2 and cos = {exp(j) + exp(-j)}/2 the final answer is exp(-2jπn/4) + j/2 exp(-jπn/4) + 1 - j/2 exp(jπn/4) +...
3. ### Periodic function

Hello, Here is something I encountered while working on a research problem. I have a function y(x + Cos[x]) = Cos[x]. Here, I am saying that y as a function of x + Cos[x] looks like a Cosine function. Here, x is the independent variable. In my problem y happens to be a displacement...
4. ### Heat equation, periodic heating of a surface

The temperature variation at the surface is described by a Fourier series \theta(t)=\sum^\infty_{n=-\infty}\theta_n e^{2\pi i n t /T} find an expression for the complex Fourier series of the temperature at depth d below the surface Solution of the diffusion equation...
5. ### Heat equation, periodic heating of a surface

The temperature variation at the surface is described by a Fourier series \theta(t)=\sum^\infty_{n=-\infty}\theta_n e^{2\pi i n t /T} find an expression for the complex Fourier series of the temperature at depth d below the surface Solution of the diffusion equation...
6. ### Which scenario describes periodic behavior?

Which scenario describes periodic behavior? A. The movement of a CD in a CD-player B. The takeoff and landing of a jet plane C. The flight of a football during a pass D. Tossing a tennis ball up into the air I know a function that repeats itself after a specific period of time is called a...
7. ### Need Help With a Few Questions.

Hi guys I am new to this forum so I am just posting a few questions because i need some help. If all answers could be explained with proofs too it would be much appreciated. 1. Solve algebraically in terms of pi: Square root of 2 times sin(x- 3pi divided by 4) add 1= 0 for 0<x<5pi...
8. ### Periodic functions reesources

Periodic Function A periodic function is an event that occurs repeatedly in a very regular manner. Suppose that you stand on the beach near a lighthouse. As you watch, the lighthouse's beam will sweep across the landscape in a very regular pattern. You might see the beam...
9. ### Which natural phenomenon is the best example of periodic behavior?

Which natural phenomenon is the best example of periodic behavior? A. Your average daily bank balance. B. The population of a city over time. C. The amount of pollution in Los Angeles as a function of time. D. The high temperature for a given city. I know that to be considered periodic...
10. ### Periodic Solution to Differential Equation

For each epsilon greater than 0, show that the differential equation x'=(x^2)-1-cos(t)-epsilon has at least one periodic solution with 0 less than x(t) less than or equal to square root of 2+epsilon
11. ### Periodic signal problem

Determine following signal is periodic if a signal is periodic,specify its fundamental period. In the class I just learn sin,cos signal In H.w. complex exponential signal..... and without fourier transform I need solution Thank you
12. ### Periodic Function

The picture shows a portion of the graph of the periodic function f(x) = sin(1 + sinx). Find the x-coordinates of the turning points P, Q, and R. Round the answers to three decimal places. Hint: The x-coordinate of Q is halfway between the x-coordinates of P and R.
13. ### Given a solution flow to find periodic solutions

Given the system of differential equations $x' = 2x + y^3$ and $y' = -y$ i found the flow $$\phi_t(x,y) = ((x_0 + 1/5y_0^3)e^{2t} - 1/5 y_0^3e^{-3t}, y_0 e^{-t})$$. I am wondering are there any periodic solutions? how do i check?
14. ### Periodic Function - Instantaneous rate of change

I started with the different quotient formula: IRoC = ( f(x+h) - f(x) ) / h , h-->0 =( 5 sin (90 +h) - 5 ) /h = (5 sin h) / h What do I do next?? I don't think I can factor out the h, even if I did what would sin take as an argument? Thank you for the help. Edit: Also, how would you apply...
15. ### Determining if solutions are periodic?

Is there a way I can determine whether or not the solutions to a (homogeneous second-order linear) differential equation are periodic just by looking at the phase plane portrait? (Will periodic solutions always be elliptical? Can spirals be periodic?)
16. ### Advanced Periodic and Exponential Functions

Please help solve using advanced periodic and exponential functions?At 9am, 5% of the students in a school have heard a rumour concerning a student-tracher relationship. By 11am, 20% of the students have heard the rumour. Find the time when 90% have heard the rumour.
17. ### periodic cycles

Can someone please explain this question, Explain why the period of a cycle is not uniquely defined, and suggest a quantity that more precisely defines what we would naturally think of as the period of a cycle. ? I am not sure about the answer, but is the period of a mathematical model not...
18. ### How do I find the period of a periodic function with a complicated expression?

For example: y=sin^2(t)(2cos(2t)+2cos(4t)+2cos(6t)+2cos(8t)+1) The period of a sin/cos function is 2Pi/B, where B is the coefficient of the argument inside the sin/cos function. However in this case, there are multiple periodic functions. Do I have to reduce them to a single periodic function...
19. ### Fractional part, periodic function

I don't know how to solve this problem: Let f be a continuous real function such that \{f(x)\} = f(\{x\}) for each x (\{x\} is the fractional part of number x) Prove that then f or f(x)-x is a periodic function. Could you help me?
20. ### Periodic Functions - Applications

I have the following equation y= -4sin15x+25 ( y represents the temperature and x represents time in hours, so x=0 means midnight and x=1 means 1:00 am) and I am given a question with the graph of the given equation, and to get the solution to the question you can you use the graph (which is...