Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the Fourier transform of e-" f(y, p, t) = * sin pt t>0, 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 I(t) = / K(t-u)V (u) du, where K(t) = af(71, P1, t)+ azf(72» P2, T). The function f(7,p,t) is as given in (a) and all the a, y (> 0) and p, are fixed parameters. By considering the Fourier transform of I(t), find the relationship that must hold between a, and az if the total net charge Q passed through the system (over a very long time) is to be zero for an arbitrary applied voltage.
Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the Fourier transform of e-" f(y, p, t) = * sin pt t>0, 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 I(t) = / K(t-u)V (u) du, where K(t) = af(71, P1, t)+ azf(72» P2, T). The function f(7,p,t) is as given in (a) and all the a, y (> 0) and p, are fixed parameters. By considering the Fourier transform of I(t), find the relationship that must hold between a, and az if the total net charge Q passed through the system (over a very long time) is to be zero for an arbitrary applied voltage.
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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Transcribed Image Text:6.
Find the Fourier transform specified in part (a) and then use it to answer part
(b).
(a) Find the Fourier transform of
e-" sin pt t> 0,
t< 0,
f(y, p, t) =
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
I(1) =
K(t - u)V(u) du,
where
K(t) = af(71, P1, t)+ azf(2, P2, t).
The function f(7, P, t) is as given in (a) and all the a, y1 (> 0) and p, are fixed
parameters. By considering the Fourier transform of I (t), find the relationship
that must hold between a, and az if the total net charge Q passed through
the system (over a very long time) is to be zero for an arbitrary applied
voltage.
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