Find the Fourier transform specified in part (a) and then use it to answer parn (b). (a) Find the Fourier transform of e-" sin pt t>0, t< 0, f(7. p.t) where y (> 0) and p are constant parameters. (b) The current I(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(y1, P1, 7) + azf(72, P2, T). The function f(y, p, t) is as given in (a) and all the a, n (> 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 parn (b). (a) Find the Fourier transform of e-" sin pt t>0, t< 0, f(7. p.t) where y (> 0) and p are constant parameters. (b) The current I(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(y1, P1, 7) + azf(72, P2, T). The function f(y, p, t) is as given in (a) and all the a, n (> 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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Question

100%

Find the Fourier transform specified in part (a) and then use it to answer parn
(b).
(a) Find the Fourier transform of
e-" sin pt t>0,
t< 0,
f(7. p.t)
where y (> 0) and p are constant parameters.
(b) The current I(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(y1, P1, 7) + azf(72, P2, T).
The function f(y, p, t) is as given in (a) and all the a, n (> 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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