Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 11.7, Problem 38P
To determine
The stiffness of the spring k for equilibrium condition of the two bars.
Investigate the stability of the system at the equilibrium position.
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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.
Homework#5
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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