Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 11.7, Problem 44P
To determine
The weight
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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 11 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 11.3 - Determine the required magnitude of force P to...Ch. 11.3 - Determine the magnitude of force P required to...Ch. 11.3 - The linkage is subjected to a force P = 2 kN....Ch. 11.3 - Prob. 4FPCh. 11.3 - Determine the angle where the 50-kg bar is in...Ch. 11.3 - Prob. 6FPCh. 11.3 - Use the method of virtual work to determine the...Ch. 11.3 - The scissors jack supports a load P. Determine the...Ch. 11.3 - If a force of P = 5 lb is applied to the handle of...Ch. 11.3 - Prob. 4P
Ch. 11.3 - Prob. 5PCh. 11.3 - Prob. 6PCh. 11.3 - When = 20, the 50-lb uniform block compresses the...Ch. 11.3 - Prob. 8PCh. 11.3 - The 4-ft members of the mechanism are pin...Ch. 11.3 - The thin rod of weight W rests against the smooth...Ch. 11.3 - If each of the three links of the mechanism have a...Ch. 11.3 - Prob. 12PCh. 11.3 - Prob. 13PCh. 11.3 - Prob. 14PCh. 11.3 - Prob. 15PCh. 11.3 - Prob. 16PCh. 11.3 - When = 30, the 25-kg uniform block compresses the...Ch. 11.3 - Prob. 18PCh. 11.3 - The Nuremberg scissors is subjected to a...Ch. 11.3 - The crankshaft is subjected to a torque of M = N ...Ch. 11.3 - Prob. 21PCh. 11.3 - The spring is unstretched when = 0. If P = 8 lb,...Ch. 11.3 - Prob. 23PCh. 11.3 - Prob. 24PCh. 11.3 - The dumpster has a weight W and a center of at...Ch. 11.7 - The potential energy of a one-degree-of-freedom...Ch. 11.7 - Prob. 27PCh. 11.7 - Prob. 28PCh. 11.7 - Prob. 29PCh. 11.7 - Prob. 30PCh. 11.7 - Prob. 31PCh. 11.7 - Prob. 32PCh. 11.7 - The uniform bar has a mass of 80 Kg. Determine the...Ch. 11.7 - The uniform bar AD has a mass of 20kg. If the...Ch. 11.7 - Prob. 35PCh. 11.7 - Prob. 36PCh. 11.7 - Determine me angle for equilibrium and...Ch. 11.7 - Prob. 38PCh. 11.7 - Prob. 39PCh. 11.7 - Prob. 40PCh. 11.7 - The uniform rod has a mass of 100 kg. If the...Ch. 11.7 - Prob. 42PCh. 11.7 - The buck has a mass of 20 Mg and a mass center at...Ch. 11.7 - Prob. 44PCh. 11.7 - Prob. 45PCh. 11.7 - Prob. 46PCh. 11.7 - Prob. 47PCh. 11.7 - Prob. 48PCh. 11.7 - Prob. 49PCh. 11.7 - Prob. 1RPCh. 11.7 - Prob. 2RPCh. 11.7 - The punch press consists of the ram R, connecting...Ch. 11.7 - Prob. 4RPCh. 11.7 - Prob. 5RPCh. 11.7 - Prob. 6RPCh. 11.7 - The uniform bar AB weighs 100 lb. If both spring...Ch. 11.7 - The spring attached to the mechanism has an...
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