Q1/ Solve the following integro-differential equation by using Laplace transform: dy(t) + 2y(t) + y(1) da = 1 – e-2t y(0) = 0 ,t > 0 dt Q2/ Find the Fourier transform for the following signal: f(1) 4 1 1 3. 4 Q3/ By using Partial Fraction Expansion method, find the inverse Z transform for the following: 2 Z F(z) = (Z – 1)(Z² + 1) Q4/ By using the properties of Laplace, find Laplace transform for the following function: sint dt f(t) = e-t %3D Q5/ Find v, (t) in the circuit shown, where i, = 5e-t u(t) A 40 2 20 mF Vo Q6/ Determine the inverse Z-transform of the following function by using Residue method. 3 – 2 z-1 + Z-2 X(z) 1- 3Z-1 + 2 Z-2

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
Q1/ Solve the following integro-differential equation by using Laplace transform:
dy(t)
+ 2y(t) +
y(1) da = 1 – e-2t y(0) = 0 ,t > 0
dt
Q2/ Find the Fourier transform for the following signal:
f(1) 4
1
1
3.
4
Q3/ By using Partial Fraction Expansion method, find the inverse Z transform for the following:
2 Z
F(z) =
(Z – 1)(Z² + 1)
Q4/ By using the properties of Laplace, find Laplace transform for the following function:
sint
dt
f(t) = e-t
%3D
Q5/ Find v, (t) in the circuit shown, where i, = 5e-t u(t) A
40 2
20 mF
Vo
Q6/ Determine the inverse Z-transform of the following function by using Residue method.
3 – 2 z-1 + Z-2
X(z)
1- 3Z-1 + 2 Z-2
Transcribed Image Text:Q1/ Solve the following integro-differential equation by using Laplace transform: dy(t) + 2y(t) + y(1) da = 1 – e-2t y(0) = 0 ,t > 0 dt Q2/ Find the Fourier transform for the following signal: f(1) 4 1 1 3. 4 Q3/ By using Partial Fraction Expansion method, find the inverse Z transform for the following: 2 Z F(z) = (Z – 1)(Z² + 1) Q4/ By using the properties of Laplace, find Laplace transform for the following function: sint dt f(t) = e-t %3D Q5/ Find v, (t) in the circuit shown, where i, = 5e-t u(t) A 40 2 20 mF Vo Q6/ Determine the inverse Z-transform of the following function by using Residue method. 3 – 2 z-1 + Z-2 X(z) 1- 3Z-1 + 2 Z-2
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