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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).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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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 applied voltage V(t) by the equation I(t) = K(t – u)V(u) du, where K(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 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.
Transcribed Image Text: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 applied voltage V(t) by the equation I(t) = K(t – u)V(u) du, where K(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 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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