Electric Motors and Control Systems
2nd Edition
ISBN: 9780073373812
Author: Frank D. Petruzella
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 3.2, Problem 4RQ
In an ideal transformer, what is the relationship between:
a. The turns ratio and the voltage ratio?
b. The voltage ratio and current ratio?
c. The primary power and secondary power?
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 3 Solutions
Electric Motors and Control Systems
Ch. 3.1 - Prob. 1RQCh. 3.1 - a. If 1 MW of electric power is to be transmitted...Ch. 3.1 - Compare the type of AC power normally supplied to...Ch. 3.1 - a. Outline the basic function of a unit...Ch. 3.1 - list three factors taken into account in selecting...Ch. 3.1 - When motors and motor controllers are installed,...Ch. 3.1 - a. What types of conduit raceways are commonly...Ch. 3.1 - Compare the function of a switchboard, panelboard,...Ch. 3.2 - Define the terms primary and secondary as they...Ch. 3.2 - On what basis is a transformer classified as being...
Ch. 3.2 - Explain how the transfer of energy takes place in...Ch. 3.2 - In an ideal transformer, what is the relationship...Ch. 3.2 - A step-down transformer with a Wins ratio of 10:1...Ch. 3.2 - A step-up transformer has a primary current of 32...Ch. 3.2 - What is meant by the term transformer magnetizing,...Ch. 3.2 - Prob. 8RQCh. 3.2 - Prob. 9RQCh. 3.2 - Prob. 10RQCh. 3.2 - The primary of a transformer is rated for 480 V...Ch. 3.2 - A single-phase transformer is rated for 0.5 kVA, a...Ch. 3.3 - Explain the way in which the high-voltage and...Ch. 3.3 - Prob. 2RQCh. 3.3 - Prob. 3RQCh. 3.3 - Prob. 4RQCh. 3.3 - Prob. 5RQCh. 3.3 - Prob. 6RQCh. 3.3 - Prob. 7RQCh. 3.3 - Prob. 8RQCh. 3.3 - Explain the basic difference between the primary...Ch. 3.3 - Prob. 10RQCh. 3.3 - Prob. 11RQCh. 3.3 - Prob. 12RQCh. 3.3 - What important safety precaution should be...Ch. 3.3 - Prob. 14RQCh. 3.3 - The control transformer for an across-the-line...Ch. 3.3 - The two primary windings of a dual-primary control...Ch. 3.3 - Prob. 3TCh. 3.3 - A dry-type general-purpose power transformer is...Ch. 3.3 - A current transformer is to be tested in circuit...Ch. 3.3 - Discuss how electric power might be distributed...Ch. 3.3 - A block of several transformers arc fed from...Ch. 3.3 - How would you proceed with a DC resistance check...Ch. 3.3 - Prob. 5DT
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