EBK MATLAB: AN INTRODUCTION WITH APPLIC
5th Edition
ISBN: 8220102007642
Author: GILAT
Publisher: YUZU
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Chapter 1, Problem 36P
Newton’s law of cooling gives the temperature T(t) of an object at time tin terms of T0, its temperature at t = 0, and the temperature of the surroundings.
A police officer arrives at a crime scene in a hotel room at 9:18 PM. where he finds a dead body. He immediately measures the body’s temperature and finds it to be 79.5°F. Exactly one hour later he measures the temperature again and finds it to be 78.0°F. Determine the time of death, assuming that victim body temperature was normal (98.6°F) prior to death and that the room temperature was constant at 69°F.
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c)
An RC circuit is given in Figure Q1.1, where Vi(t) and Vo(t) are the input and
output voltages.
(i) Derive the transfer function of the circuit.
(ii) With a unit step change of Vi(t) applied to the circuit, derive the time
response of Vo(t) with this step change.
Vi(t)
C₁
Vo(1)
R₂ C2 C3 |
R = 20 ΚΩ = 50 ΚΩ
C=C2=C3=25 μF
Figure Q1.1. RC circuit.
c) An RC circuit is given in Figure Q1. vi(t) and vo (t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii) With a unit step change vi(t) applied to the circuit, derive and sketch the
time response of the circuit.
R₁ R2
v₁(t)
R3 C₁
v₁(t)
R₁ = R₂ = 10 k
R3
= 100 kn C₁ = 100 μF
Figure Q1. RC circuit.
c)
A RC circuit is given in Figure Q1.1. Vi(t) and Vo(t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii)
With a unit step change of Vi(t) applied to the circuit, derive the time
response of the circuit.
C₁ C₂
Vi(t)
Vo(1)
R₁ C₂
R-25 k C=C2=50 µF
Figure Q1.1. RC circuit.
Chapter 1 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
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