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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 off(y, p, t)Jet sin pt t> 0,0'0>1where y (> 0) and p are constant parameters.(b) The current 1(t) flowing through a certain system is related to the appliedvoltage V(t) by the equationArosI(t)=K(t - u)V(u) du,wherenOrK(t) = aif (y1, Pi, T) + a2f(72, P2, T).The function f(y, p, t) is as given in (a) and all the ai, yi (> 0) and pi are fixedparameters. By considering the Fourier transform of I (t), find the relationshipthat must hold between ai and a2 if the total net charge Q passed throughthe system (over a very long time) is to be zero for an arbitrary appliedvoltage.

Question
Find the Fourier transform specified in part (a) and then use it to answer part
(b).
(a) Find the Fourier transform of
f(y, p, t)Jet sin pt t> 0,
0
'0>1
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
Aros
I(t)=
K(t - u)V(u) du,
where
nOr
K(t) = aif (y1, Pi, T) + a2f(72, P2, T).
The function f(y, p, t) is as given in (a) and all the ai, yi (> 0) and pi are fixed
parameters. By considering the Fourier transform of I (t), find the relationship
that must hold between ai and a2 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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Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the Fourier transform of f(y, p, t)Jet sin pt t> 0, 0 '0>1 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 Aros I(t)= K(t - u)V(u) du, where nOr K(t) = aif (y1, Pi, T) + a2f(72, P2, T). The function f(y, p, t) is as given in (a) and all the ai, yi (> 0) and pi are fixed parameters. By considering the Fourier transform of I (t), find the relationship that must hold between ai and a2 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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check_circleAnswer
Step 1

(a)

Consider the provided function.

e" sin pt
t> 0
f(y,p.t)
0
t<0
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e" sin pt t> 0 f(y,p.t) 0 t<0

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Step 2

The provided function can be written as:

f (y.p.t) e
sin pt v (t)
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f (y.p.t) e sin pt v (t)

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Step 3

Now

...
Z(p)-f+p)]
sin pt v(t
sin pt v(t)
5-p)-of+p)]
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Z(p)-f+p)] sin pt v(t sin pt v(t) 5-p)-of+p)]

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Advanced Math

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