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 8, Problem 57RQ
To determine
The common name given to ceramic at the amorphous or non-crystalline state.
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If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.
Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.
Discuss the positive definiteness of V (x, x_dot).
Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of thesystem based on the information we gain from ̇V_dot .
In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
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Chapter 8 Solutions
DeGarmo's Materials and Processes in Manufacturing
Ch. 8 - Discuss the terms plastics and polymers. In...Ch. 8 - What are some naturally occurring nonmetallic...Ch. 8 - What are some material families that would be...Ch. 8 - How might plastics be defined from the viewpoints...Ch. 8 - What is the primary type of atomic bonding within...Ch. 8 - What is the difference between a saturated and an...Ch. 8 - What is an isomer?Ch. 8 - Describe and differentiate the two means of...Ch. 8 - What is a mer?Ch. 8 - What is degree of polymerization?
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