Problem 4. In class (or see notes on the homepage), we worked out the Fourier series for a square...
Fourier Series (10.3.05) The function plotted below is f(x)2whenand zero otherwise. This function can be approximated on the interval [-1,1] by the function (a) Find the values of an, αι, α2, α3, and α4 using the integrals given in class. (Hint 1: Use the symmetry of f(x) so that you only need to integrate over positive values of x. Hint 2: To evaluate an for n 1,2,3,4, do the integration without plugging in n. Once you have done the integral...
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
1. This quasi-"walkthrough" problem is great practice in cross-products, vectors, and integration. Consider the current loop shown in Figure 2, with B _Bx, and the loop lying in the x - z plane of the page (y points into the page). We wish to find the net torque on this current loop. we'll do this by integrating in θ, the angle shown (a) We'll start with a little segment dl at point p as shown in the figure. What is...
Problem 4.1 - Odd Bound States for the Finite Square Well Consider the finite square well potential of depth Vo, V(x) = -{ S-V., –a sx sa 10, else In lecture we explored the even bound state solutions for this potential. In this problem you will explore the odd bound state solutions. Consider an energy E < 0 and define the (real, positive) quantities k and k as 2m E K= 2m(E + V) h2 h2 In lecture we wrote...
(4) Let V and W be vector spaces over R: consider the free vector space F(V × W) on the Cartesian product V x W of V and W. Given an element (v, w) of V x W, we view (v, w) as an element of F(V x W) via the inclusion map i : V x W F(V x W) Any element of F(V x W) is a finite linear combination of such elements (v, w) Warning. F(V ×...
MTH133 Lab 5: Pre-Lab Learning Goals In class, typical examples of divergent sequences and series are those whose values fly off to infinity. In real life, however, divergence is more frequently associated with meandering behavior that doesn't fly off to infinity but also doesn't settle down toward one number. The simplest example of this is the eyclical behavior of the sequence 2 1,-1,1, 1, 1,-1,... which remains always bounded but nevertheless does not converge. Real-life examples of bounded divergent sequences...
Please be specific, thanks! (2) Why First-Order Systems (of a Specific Form) Are Sufficient: In class I stated that all systems of differential equations can be turned into first-order systems. And I wrote that first-order systems can be written in the form: For 3-by-3 system, the form is: r-f(r, y,z,t) y- g(x, y, z, t) , = h(z,y,z, This can be generalized to any number of unknown functions. a) Notice that r', y', and z are not included in the...
please answer "class playerexception(exception):" in python Notes Two players will face each other. They each decide independently to "cooperate" or "cheat". If they both cooperated, they each win two points. If they both cheated, nobody wins anything. one cheats, the cheater gets +3 and the cooperator loses a point. That wasn't very kind! One turn is defined as each player making a choice, and winning or losing some points as a result. Shared history against this player is available to...
Create a NOTEPAD or PDF file that restates the problem in your own words, specifies what input is needed, what output is expected, the step by step process (algorithm) to get the output from the input, and test data (input for which you know the expected output) for each of the 3 problems given below. You should not write any actual C++ code. Make sure the problem statement is in your own words and is descriptive enough so someone not...
Help C++ Write a string class. To avoid conflicts with other similarly named classes, we will call our version MyString. This object is designed to make working with sequences of characters a little more convenient and less error-prone than handling raw c-strings, (although it will be implemented as a c-string behind the scenes). The MyString class will handle constructing strings, reading/printing, and accessing characters. In addition, the MyString object will have the ability to make a full deep-copy of itself...