Find the Fourier transform specified in part (a) and then use it to answer part(b).(a) Find the Fourier transform of" sin pt t>0,t< 0,f(r. p, t) =where y (> 0) and p are constant parameters.(b) The current I(t) flowing through a certain system is related to the appliedvoltage V(t) by the equationI(t) =K(t – u)V(u) du,whereK(t) = a¡f(71, P1,t) + azf(y2, P2, t).The function f(y, p, t) is as given in (a) and all the a;, y¡ (> 0) and p, are fixedparameters. By considering the Fourier transform of I(t), find the relationshipthat must hold between a, and az if the total net charge Q passed throughthe system (over a very long time) is to be zero for an arbitrary appliedvoltage.

In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt t>0,0…

Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the Fourier transform of ' sin pt t>0, | 0 f(y, p, t) = t< 0, where y (> 0) and p are constant parameters. (b) The current 1(t) flowing through a certain system is related to the applied voltage V(t) by the equation =| K(t– u)V(u) du, where K(7) = a¡f(71, P1, t) + azf(72, P2, T).

Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the Fourier transform of ' sin pt t>0, | 0 f(y, p, t) = t< 0, where y (> 0) and p are constant parameters. (b) The current 1(t) flowing through a certain system is related to the applied voltage V(t) by the equation =| K(t– u)V(u) du, where K(7) = a¡f(71, P1, t) + azf(72, P2, T).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Prove that the Fourier transform of f") (x), the nth derivative of f(x) is (- ip) times the Fourier transform of f(x) provided that the first (n – 1) derivatives of f(x) vanish as x→to.
a) Find the Fourier Transform of f(x) √2лx³ ex = 2πx³еx, 0
3) find the fourier transform y(t) = x (t). Cosuit Y(f) = ?
Q3) Verify that the Fourier transform of the function [1-x|, |x|1 a. Then Show that 2 sin u sin u b. Compute the integral 2 du sinu u is T 4 4 du sin² 2² (k/2) (4/2)² ƒ(k)=
The Fourier transform of a continuous-time function x(t) is X (f) = x(t)e-1²nft dt