Signal and system Three different systems are described below through their input-output relationships. Foreach, determine whether the system is time-invariant or not:a.g(t)=5x(t)b. y(t) = 3 cos (z (t))y (t) = 3 cos (t) r(t)c.R₁node 1(1)Fig. P2.1. RC circuit consisting oftwo resistors (R, and R₂) and acapacitor C.Cic(0)yinin (1/2Fig. P2.2. Resonator in an AM modulator.+C2.1 The electrical circuit shown in Fig. P2.1 consists of two resistors R₁ andR₂ and a capacitor C.(i) Determine the differential equation relating the input voltage Vin (1) tothe output voltage Vout(1).(ii) Determine whether the system is (a) linear, (b) time-invariant;2.2 The resonant circuit shown in Fig. P2.2 is generally used as a resonator inan amplitude modulation (AM) system.(i) Determine the relationship between the input i(t) and the output v(t)of the AM modulator.(ii) Determine whether the system is (a) linear, (b) time-invariant;

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Three different systems are described below through their input-output relationships. For each, determine whether the system is time-invariant or not: a. g(t)=5r(t) b. y(t) = 3 cos (z (t)) c. y (t) = 3 cos (t) r(t)

Three different systems are described below through their input-output relationships. For each, determine whether the system is time-invariant or not: a. g(t)=5r(t) b. y(t) = 3 cos (z (t)) c. y (t) = 3 cos (t) r(t)

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

Signal and system

Three different systems are described below through their input-output relationships. For
each, determine whether the system is time-invariant or not:
a.
g(t)=5x(t)
b. y(t) = 3 cos (z (t))
y (t) = 3 cos (t) r(t)
c.
R₁
node 1
(1)
Fig. P2.1. RC circuit consisting of
two resistors (R, and R₂) and a
capacitor C.
C
ic(0)
yinin (
1/2
Fig. P2.2. Resonator in an AM modulator.
+C
2.1 The electrical circuit shown in Fig. P2.1 consists of two resistors R₁ and
R₂ and a capacitor C.
(i) Determine the differential equation relating the input voltage Vin (1) to
the output voltage Vout(1).
(ii) Determine whether the system is (a) linear, (b) time-invariant;
2.2 The resonant circuit shown in Fig. P2.2 is generally used as a resonator in
an amplitude modulation (AM) system.
(i) Determine the relationship between the input i(t) and the output v(t)
of the AM modulator.
(ii) Determine whether the system is (a) linear, (b) time-invariant;

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