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a) Find the Fourier series expansion for f(x) =1- x2; 0< x < 1. b) Find the eigenvalues and eigenfunctions of the boundary value problem y" + ay = 0, y' (0) = 0, y () = 0. Evaluate all cases. c) The charge on the capacitor in an LRC-series circuit when R = 100k 2, L = k H, C = 4 x 10$ F and E(t) = 25 V is q(t) = c,e-50t cos 150t + cze-50t sin 150t + 0.001 where k is a constant. Find the value of k and the charge on the capacitor at t = 0.01s

a) Find the Fourier series expansion for f(x) =1- x2; 0< x < 1. b) Find the eigenvalues and eigenfunctions of the boundary value problem y" + ay = 0, y' (0) = 0, y () = 0. Evaluate all cases. c) The charge on the capacitor in an LRC-series circuit when R = 100k 2, L = k H, C = 4 x 10$ F and E(t) = 25 V is q(t) = c,e-50t cos 150t + cze-50t sin 150t + 0.001 where k is a constant. Find the value of k and the charge on the capacitor at t = 0.01s

Advanced Engineering Mathematics
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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a) Find the Fourier series expansion for f(x) = 1-x²; 0< x < 1. b) Find the eigenvalues and eigenfunctions of the boundary value problem y" + ay = 0, y'(0) = 0, y () = 0. Evaluate all cases. c) The charge on the capacitor in an LRC-series circuit when R = 100k 2, L = k H, C = 4 x 10$ F and E(t) = 25 V is q(t) = c,e-50t cos 150t + c2e-50t sin 150t + 0.001 where k is a constant. Find the value of k and the charge on the capacitor at t= 0.01s when q(0) 0 C and i(0) = 0 A.
Transcribed Image Text:a) Find the Fourier series expansion for f(x) = 1-x²; 0< x < 1. b) Find the eigenvalues and eigenfunctions of the boundary value problem y" + ay = 0, y'(0) = 0, y () = 0. Evaluate all cases. c) The charge on the capacitor in an LRC-series circuit when R = 100k 2, L = k H, C = 4 x 10$ F and E(t) = 25 V is q(t) = c,e-50t cos 150t + c2e-50t sin 150t + 0.001 where k is a constant. Find the value of k and the charge on the capacitor at t= 0.01s when q(0) 0 C and i(0) = 0 A.
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