Degarmo's Materials And Processes In Manufacturing
13th Edition
ISBN: 9781119492825
Author: Black, J. Temple, Kohser, Ronald A., Author.
Publisher: Wiley,
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Chapter 12, Problem 3CS
Is the dashed line in the figure labeled “mean” the mean or the average? (The mean is
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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 12 Solutions
Degarmo's Materials And Processes In Manufacturing
Ch. 12 - Define accuracy or precision in terms of a...Ch. 12 - What does the nature of the process refer to?Ch. 12 - Suppose you have a pistol�shooting process that...Ch. 12 - Review the steps required to make a PC study of a...Ch. 12 - Why do not standard tables exist detailing the...Ch. 12 - Here are some common, everyday processes with...Ch. 12 - Why might the diameter measurements for holes...Ch. 12 - What are some common manufactured items that may...Ch. 12 - What are common reasons for sampling inspection...Ch. 12 - Fill in this table with one of the four following...
Ch. 12 - Now explain why when we sample, we cannot avoid...Ch. 12 - Which error can lead to legal action from the...Ch. 12 - Define and explain the difference between andX and...Ch. 12 - What is Cp, and why is a value of 0.80 not good?...Ch. 12 - Prob. 15RQCh. 12 - What are some of the alternatives available to you...Ch. 12 - Cpk is another process capability index. How does...Ch. 12 - In a sigma chart, are σ values for the samples...Ch. 12 - What is an assignable cause, and how is it...Ch. 12 - Why is the range used to measure variability when...Ch. 12 - How is the standard deviation of a distribution of...Ch. 12 - In the last two decades, the quality in...Ch. 12 - Figure 12.15 shows a bimodal check sheet...Ch. 12 - Control charts use upper and lower control limits....Ch. 12 - In Figure 12.10, what are the USL and the LSL,...Ch. 12 - What are four major branches (fishbones) on a...Ch. 12 - How does variation in the measuring device...Ch. 12 - What are Taguchi or factorial experiments, and how...Ch. 12 - How does the Taguchi approach differ from the...Ch. 12 - Why are Taguchi experiments so important compared...Ch. 12 - Explain what happed to improve the process inÂ...Ch. 12 - In Table 12.1, explain MOâ€�COâ€�MOO....Ch. 12 - What is a quality circle, and how might you apply...Ch. 12 - Which of the seven QC tools is being used inÂ...Ch. 12 - Go to a subway restaurant and develop a process...Ch. 12 - What do you estimate the standard deviation of...Ch. 12 - Is the dashed line in the figure labeled mean the...Ch. 12 - From the information given in the discussion and...Ch. 12 - What is the most glaring error in the figure, and...
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