DeGarmo's Materials and Processes in Manufacturing
12th Edition
ISBN: 9781118987674
Author: J. T. Black, Ronald A. Kohser
Publisher: WILEY
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Chapter 31, Problem 6RQ
Explain the meaning of
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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 31 Solutions
DeGarmo's Materials and Processes in Manufacturing
Ch. 31 - How does the pitch diameter differ from the major...Ch. 31 - Prob. 2RQCh. 31 - Prob. 3RQCh. 31 - Prob. 4RQCh. 31 - Prob. 5RQCh. 31 - Explain the meaning of 14 -20 UNC-3A.Ch. 31 - Prob. 7RQCh. 31 - Prob. 8RQCh. 31 - Prob. 9RQCh. 31 - Prob. 10RQ
Ch. 31 - Prob. 11RQCh. 31 - Prob. 12RQCh. 31 - Prob. 13RQCh. 31 - What is the reason for using a taper tap before a...Ch. 31 - Prob. 15RQCh. 31 - Can a fluteless tap be used for threading a hole...Ch. 31 - What provisions should a designer make so that a...Ch. 31 - What is the major advantage of a spiral-point tap?Ch. 31 - Prob. 19RQCh. 31 - Is it desirable for a tapping fluid to have...Ch. 31 - How does thread milling differ from thread...Ch. 31 - What are the advantages of making threads by...Ch. 31 - Prob. 23RQCh. 31 - Prob. 24RQCh. 31 - What is a fluteless tap?Ch. 31 - Why is the involute form used for gear teeth?Ch. 31 - What is the diametral pitch of a gear?Ch. 31 - What is the relationship between the diametral...Ch. 31 - On a sketch of a gear, indicate the pitch circle,...Ch. 31 - What five requirements must be met for gears to...Ch. 31 - What are the advantages of helical gears compared...Ch. 31 - Prob. 32RQCh. 31 - What difficulty would be encountered in bobbing a...Ch. 31 - What is the only type of machine on which...Ch. 31 - Prob. 35RQCh. 31 - Why arent more gears made by broaching?Ch. 31 - What is the most important property of a crown...Ch. 31 - What are three basic processes for machining...Ch. 31 - Which basic gear-machining process is utilized in...Ch. 31 - When a helical gear is machined on a milling...Ch. 31 - Why is a gear-hobbing machine much more productive...Ch. 31 - Prob. 42RQCh. 31 - What are the advantages of cold-roll forming for...Ch. 31 - Prob. 44RQCh. 31 - Under what conditions should shaving not be used...Ch. 31 - Prob. 46RQCh. 31 - Can lapping be used to finish cast iron gears?Ch. 31 - What factors are usually checked in inspecting...Ch. 31 - What are the basic methods for gear finishing?Ch. 31 - A hob that has a pitch diameter of 76.2 mm is used...Ch. 31 - In Figure 31.17, a form-milling operation and...Ch. 31 - A gear-broaching machine can complete the gear in...Ch. 31 - Prob. 4PCh. 31 - If only three gears described in Problem 4 were to...Ch. 31 - Based on the size and shape of the product,...Ch. 31 - What type of engineering materials might be able...Ch. 31 - Prob. 3CS
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