EOCP 4.6 Figure 4.15Use the Fourier transform to find y(t), a particular solution, in each of the systems shown in Figures 4.15u(1)eu(t)Heu(t)Σy (1)

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Answered: Use the Fourier transform to find y(t),…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Section 2-6 : Chain Rule - Practice Problems dz 1. Given the following information use the Chain Rule to determine dt cos (yz") z= t - 2t, y= 1-t
2. Consider an ODE of the form:x2y′′+axy′+by = 0 with given constants a and b and unknown solution y(x). Assuming that y(x) follows the form y=xm, perform the following tasks:a.) Solve for y′(x) and y′′(x) and transform the given ODE in terms of x,m,a, and b.b.) Determine the characteristic equation of the ODE.
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1. The Fourier coefficients of a system with period T are bm =me-m/3 and all am = 0. What is the frequency of the highest energy mode? 2. An even function f(t) has Fourier coefficients ao = 1 and an = and period 27. Use Parseval's theorem to evaluate f f(t)|²dt? [hint, Σ=1** - 17] -
6. Use the Fourier analysis method to discuss the stability of the Crank-Nicolson method λ (1 + 2)Ui,j+1 − ½ (Ui+1,j+1 + U₁−1,;j+1) = (1 − A)Uij + ½ (Ui+1; + Ui−1,)). 2 2
Write the system of differential equations given in the question in the normal form defined as in the 3rd photo and solve the resulting system through the eigenvalues and eigen-vectors of the square matrix A.

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Use the Fourier transform to find y(t), a particular solution, in each of the systems shown in Figures 4.15 u(1) eu(t) H 5 eu(1) Σ y(1)