Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 15.2, Problem 28P
To determine
The position of the crate vertically upward when t reaches to 3 s:
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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 15 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 15.2 - Determine the impulse of the force for t = 2 s.Ch. 15.2 - The 0.5kg ball strikes the rough ground and...Ch. 15.2 - Prob. 2FPCh. 15.2 - Prob. 3FPCh. 15.2 - The wheels of the 1.5-Mg car generate the traction...Ch. 15.2 - Prob. 5FPCh. 15.2 - A man kicks the 150-g ball such that it leaves the...Ch. 15.2 - If the coefficient of kinetic friction between the...Ch. 15.2 - Prob. 3PCh. 15.2 - Each of the cables can sustain a maximum tension...
Ch. 15.2 - A hockey puck is traveling to the left with a...Ch. 15.2 - A train consists of a 50-Mg engine and three cars,...Ch. 15.2 - Crates A and B weigh 100 lb and 50 lb,...Ch. 15.2 - Prob. 8PCh. 15.2 - Prob. 9PCh. 15.2 - The 50-kg crate is pulled by the constant force P....Ch. 15.2 - During operation the jack hammer strikes the...Ch. 15.2 - For a short period of time, the frictional driving...Ch. 15.2 - The 2.5-Mg van is traveling with a speed of 100...Ch. 15.2 - Prob. 14PCh. 15.2 - Prob. 15PCh. 15.2 - The choice of a seating material for moving...Ch. 15.2 - The towing force acting on the 400-kg safe varies...Ch. 15.2 - Prob. 18PCh. 15.2 - Prob. 19PCh. 15.2 - Prob. 20PCh. 15.2 - If it takes 35 s for the 50-Mg tugboat to increase...Ch. 15.2 - Prob. 22PCh. 15.2 - Prob. 23PCh. 15.2 - The motor pulls on the cable at A with a force F =...Ch. 15.2 - The balloon has a total mass of 400 kg including...Ch. 15.2 - Prob. 26PCh. 15.2 - Prob. 27PCh. 15.2 - Prob. 28PCh. 15.2 - Prob. 29PCh. 15.2 - Prob. 30PCh. 15.2 - Prob. 31PCh. 15.2 - Prob. 32PCh. 15.2 - The log has a mass of 500 kg and rests on the...Ch. 15.2 - Prob. 34PCh. 15.2 - Prob. 7FPCh. 15.2 - The cart and package have a mass of 20 kg and 5...Ch. 15.3 - The 5-kg block A has an initial speed of 5 m/s as...Ch. 15.3 - Prob. 10FPCh. 15.3 - Prob. 11FPCh. 15.3 - The cannon and support without a projectile have a...Ch. 15.3 - The 5-Mg bus B is traveling to the right at 20...Ch. 15.3 - Prob. 36PCh. 15.3 - A railroad car having a mass of 15 Mg is coasting...Ch. 15.3 - A ballistic pendulum consists of a 4-kg wooden...Ch. 15.3 - Prob. 40PCh. 15.3 - A 0.03-lb bullet traveling at 1300 ft/s strikes...Ch. 15.3 - A 0.03-lb bullet traveling at 1300 ft/s strikes...Ch. 15.3 - Prob. 43PCh. 15.3 - Prob. 44PCh. 15.3 - Prob. 45PCh. 15.3 - The two blocks A and B each have a mass of 5 kg...Ch. 15.3 - The 30-Mg freight car A and 15-Mg freight car B...Ch. 15.3 - Blocks A and B have masses of 40 kg and 60 kg,...Ch. 15.3 - Prob. 49PCh. 15.3 - Prob. 50PCh. 15.3 - Prob. 51PCh. 15.3 - The free-rolling ramp has a mass of 40 kg. A 10-kg...Ch. 15.3 - Block A has a mass of 5 kg and is placed on the...Ch. 15.3 - Solve Prob. 15-53 if the coefficient of kinetic...Ch. 15.3 - Prob. 55PCh. 15.3 - Prob. 56PCh. 15.3 - The 10-kg block is held at rest on the smooth...Ch. 15.3 - Prob. 13FPCh. 15.3 - Prob. 14FPCh. 15.4 - The 30-lb package A has a speed of 5 ft/s when it...Ch. 15.4 - The ball strikes the smooth wall with a velocity...Ch. 15.4 - Prob. 17FPCh. 15.4 - Prob. 18FPCh. 15.4 - Prob. 58PCh. 15.4 - Prob. 59PCh. 15.4 - Disk A has a mass of 2 kg and is sliding forward...Ch. 15.4 - Prob. 61PCh. 15.4 - Prob. 62PCh. 15.4 - Prob. 63PCh. 15.4 - Prob. 64PCh. 15.4 - A 1-lb ball A is traveling horizontally at 20 ft/s...Ch. 15.4 - Block A, having a mass m, is released from rest,...Ch. 15.4 - Prob. 67PCh. 15.4 - Prob. 68PCh. 15.4 - Prob. 69PCh. 15.4 - Prob. 70PCh. 15.4 - Prob. 71PCh. 15.4 - The tennis ball is struck with a horizontal...Ch. 15.4 - Prob. 73PCh. 15.4 - Two smooth disks A and B each have a mass of 0.5...Ch. 15.4 - Prob. 75PCh. 15.4 - Prob. 76PCh. 15.4 - The cue ball A is given an initial velocity (vA)1...Ch. 15.4 - Prob. 78PCh. 15.4 - Prob. 79PCh. 15.4 - A ball of negligible size and mass m is given a...Ch. 15.4 - Prob. 81PCh. 15.4 - The 20-lb box slides on the surface for which k =...Ch. 15.4 - Prob. 83PCh. 15.4 - Prob. 84PCh. 15.4 - Prob. 85PCh. 15.4 - Prob. 86PCh. 15.4 - Prob. 87PCh. 15.4 - Prob. 88PCh. 15.4 - Prob. 89PCh. 15.4 - Prob. 90PCh. 15.4 - The 200-g billiard ball is moving with a speed of...Ch. 15.4 - Prob. 92PCh. 15.4 - Disks A and B have a mass of 15 kg and 10 kg,...Ch. 15.4 - Prob. 19FPCh. 15.4 - Prob. 20FPCh. 15.7 - Initially the 5-kg block is moving with a constant...Ch. 15.7 - Prob. 22FPCh. 15.7 - Prob. 23FPCh. 15.7 - Prob. 24FPCh. 15.7 - Determine the angular momentum HO of the 6-lb...Ch. 15.7 - Determine the angular momentum HP of the 6-lb...Ch. 15.7 - Prob. 96PCh. 15.7 - Determine the angular momentum Hp, of each of the...Ch. 15.7 - Prob. 98PCh. 15.7 - Determine the angular momentum Hp of the 3-kg...Ch. 15.7 - Each ball has a negligible size and a mass of 10...Ch. 15.7 - The 800-lb roller-coaster car starts from rest on...Ch. 15.7 - The 800-lb roller-coaster car starts from rest on...Ch. 15.7 - A 4-lb ball B is traveling around in a circle of...Ch. 15.7 - A 4-lb ball B is traveling around in a circle of...Ch. 15.7 - The two blocks A and B each have a mass of 400 g....Ch. 15.7 - A small particle having a mass m is placed inside...Ch. 15.7 - If the rod of negligible mass is subjected to a...Ch. 15.7 - When the 2-kg bob is given a horizontal speed of...Ch. 15.7 - The elastic cord has an unstretched length l0 =...Ch. 15.7 - The amusement park ride consists of a 200-kg car...Ch. 15.7 - Prob. 111PCh. 15.7 - Prob. 112PCh. 15.7 - An earth satellite of mass 700 kg is launched into...Ch. 15.7 - Prob. 114PCh. 15.9 - Prob. 115PCh. 15.9 - Prob. 116PCh. 15.9 - Prob. 117PCh. 15.9 - Prob. 118PCh. 15.9 - Prob. 119PCh. 15.9 - The gauge pressure of water at A is 150.5 kPa....Ch. 15.9 - Prob. 121PCh. 15.9 - The fountain shoots water in the direction shown....Ch. 15.9 - A plow located on the front of a locomotive scoops...Ch. 15.9 - Prob. 124PCh. 15.9 - Water is discharged from a nozzle with a velocity...Ch. 15.9 - Prob. 126PCh. 15.9 - Prob. 127PCh. 15.9 - Prob. 128PCh. 15.9 - The water flow enters below the hydrant at C at...Ch. 15.9 - Sand drops onto the 2-Mg empty rail car at 50 kg/s...Ch. 15.9 - Prob. 131PCh. 15.9 - Prob. 132PCh. 15.9 - Prob. 133PCh. 15.9 - A rocket has an empty weight of 500 lb and carries...Ch. 15.9 - Prob. 135PCh. 15.9 - The rocket car has a mass of 2 Mg (empty) and...Ch. 15.9 - Prob. 137PCh. 15.9 - Prob. 138PCh. 15.9 - The missile weighs 40 000 lb. The constant thrust...Ch. 15.9 - Prob. 140PCh. 15.9 - Prob. 141PCh. 15.9 - The 12-Mg jet airplane has a constant speed of 950...Ch. 15.9 - Prob. 143PCh. 15.9 - Prob. 144PCh. 15.9 - Prob. 145PCh. 15.9 - Prob. 146PCh. 15.9 - Prob. 147PCh. 15.9 - Prob. 148PCh. 15.9 - Prob. 149PCh. 15.9 - Prob. 1CPCh. 15.9 - Prob. 2CPCh. 15.9 - Prob. 1RPCh. 15.9 - Prob. 2RPCh. 15.9 - Prob. 3RPCh. 15.9 - Prob. 4RPCh. 15.9 - The 200-g projectile is fired with a velocity of...Ch. 15.9 - Block A has a mass of 3 kg and is sliding on a...Ch. 15.9 - Two smooth billiard balls A and B have an equal...Ch. 15.9 - Prob. 8RP
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