Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)
Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137503520
Author: Serope Kalpakjian, Steven Schmid
Publisher: PEARSON+
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Chapter 6, Problem 6.94P
To determine

The relationship between workpiece height and velocity.

The sketch of the velocity profile for the hammer.

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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 6 Solutions

Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)

Ch. 6 - Prob. 6.11QCh. 6 - Prob. 6.12QCh. 6 - Prob. 6.13QCh. 6 - Prob. 6.14QCh. 6 - Prob. 6.15QCh. 6 - Prob. 6.16QCh. 6 - Prob. 6.17QCh. 6 - Prob. 6.18QCh. 6 - Prob. 6.19QCh. 6 - Prob. 6.20QCh. 6 - Prob. 6.21QCh. 6 - Prob. 6.22QCh. 6 - Prob. 6.23QCh. 6 - Prob. 6.24QCh. 6 - Prob. 6.25QCh. 6 - Prob. 6.26QCh. 6 - Prob. 6.27QCh. 6 - Prob. 6.28QCh. 6 - Prob. 6.29QCh. 6 - Prob. 6.30QCh. 6 - Prob. 6.31QCh. 6 - Prob. 6.32QCh. 6 - Prob. 6.33QCh. 6 - Prob. 6.34QCh. 6 - Prob. 6.35QCh. 6 - Prob. 6.36QCh. 6 - Prob. 6.37QCh. 6 - Prob. 6.38QCh. 6 - Prob. 6.39QCh. 6 - Prob. 6.40QCh. 6 - Prob. 6.41QCh. 6 - Prob. 6.42QCh. 6 - Prob. 6.43QCh. 6 - Prob. 6.44QCh. 6 - Prob. 6.45QCh. 6 - Prob. 6.46QCh. 6 - Prob. 6.47QCh. 6 - Prob. 6.48QCh. 6 - Prob. 6.49QCh. 6 - Prob. 6.50QCh. 6 - Prob. 6.51QCh. 6 - Prob. 6.52QCh. 6 - Prob. 6.53QCh. 6 - Prob. 6.54QCh. 6 - Prob. 6.55QCh. 6 - Prob. 6.56QCh. 6 - Prob. 6.57QCh. 6 - Prob. 6.58QCh. 6 - Prob. 6.59QCh. 6 - Prob. 6.60QCh. 6 - Prob. 6.61QCh. 6 - Prob. 6.62QCh. 6 - Prob. 6.63QCh. 6 - Prob. 6.64QCh. 6 - Prob. 6.65QCh. 6 - Prob. 6.66QCh. 6 - Prob. 6.67QCh. 6 - Prob. 6.68QCh. 6 - Prob. 6.69QCh. 6 - Prob. 6.70QCh. 6 - Prob. 6.71QCh. 6 - Prob. 6.72QCh. 6 - Prob. 6.73PCh. 6 - Prob. 6.74PCh. 6 - Prob. 6.75PCh. 6 - Prob. 6.76PCh. 6 - Prob. 6.77PCh. 6 - Prob. 6.78PCh. 6 - Prob. 6.79PCh. 6 - Prob. 6.80PCh. 6 - Prob. 6.81PCh. 6 - Prob. 6.82PCh. 6 - Prob. 6.83PCh. 6 - Prob. 6.84PCh. 6 - Prob. 6.85PCh. 6 - Prob. 6.86PCh. 6 - Prob. 6.87PCh. 6 - Prob. 6.88PCh. 6 - Prob. 6.89PCh. 6 - Prob. 6.90PCh. 6 - Prob. 6.91PCh. 6 - Prob. 6.92PCh. 6 - Prob. 6.93PCh. 6 - Prob. 6.94PCh. 6 - Prob. 6.95PCh. 6 - Prob. 6.96PCh. 6 - Prob. 6.97PCh. 6 - Prob. 6.98PCh. 6 - Prob. 6.99PCh. 6 - Prob. 6.100PCh. 6 - Prob. 6.101PCh. 6 - Prob. 6.102PCh. 6 - Prob. 6.103PCh. 6 - Prob. 6.104PCh. 6 - Prob. 6.105PCh. 6 - Prob. 6.106PCh. 6 - Prob. 6.107PCh. 6 - Prob. 6.108PCh. 6 - Prob. 6.109PCh. 6 - Prob. 6.110PCh. 6 - Prob. 6.111PCh. 6 - Prob. 6.112PCh. 6 - Prob. 6.113PCh. 6 - Prob. 6.114PCh. 6 - Prob. 6.115PCh. 6 - Prob. 6.116PCh. 6 - Prob. 6.117PCh. 6 - Prob. 6.118PCh. 6 - Prob. 6.119PCh. 6 - Prob. 6.120PCh. 6 - Prob. 6.121PCh. 6 - Prob. 6.122PCh. 6 - Prob. 6.123PCh. 6 - Prob. 6.124PCh. 6 - Prob. 6.125PCh. 6 - Prob. 6.126PCh. 6 - Prob. 6.127PCh. 6 - Prob. 6.128PCh. 6 - Prob. 6.129PCh. 6 - Prob. 6.130PCh. 6 - Prob. 6.131PCh. 6 - Prob. 6.132PCh. 6 - Prob. 6.133PCh. 6 - Prob. 6.134PCh. 6 - Prob. 6.135PCh. 6 - Prob. 6.136PCh. 6 - Prob. 6.137PCh. 6 - Prob. 6.138PCh. 6 - Prob. 6.139PCh. 6 - Prob. 6.140PCh. 6 - Prob. 6.142DCh. 6 - Prob. 6.143DCh. 6 - Prob. 6.144DCh. 6 - Prob. 6.145DCh. 6 - Prob. 6.146DCh. 6 - Prob. 6.147DCh. 6 - Prob. 6.149D
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