
THERMODYNAMICS (LL)-W/ACCESS >CUSTOM<
9th Edition
ISBN: 9781266657610
Author: CENGEL
Publisher: MCG CUSTOM
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Chapter 2.8, Problem 84P
To determine
The extra amount of
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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 2 Solutions
THERMODYNAMICS (LL)-W/ACCESS >CUSTOM<
Ch. 2.8 - What is the difference between the macroscopic and...Ch. 2.8 - What is total energy? Identify the different forms...Ch. 2.8 - List the forms of energy that contribute to the...Ch. 2.8 - How are heat, internal energy, and thermal energy...Ch. 2.8 - What is mechanical energy? How does it differ from...Ch. 2.8 - Portable electric heaters are commonly used to...Ch. 2.8 - Natural gas, which is mostly methane CH4, is a...Ch. 2.8 - Consider the falling of a rock off a cliff into...Ch. 2.8 - Electric power is to be generated by installing a...Ch. 2.8 - The specific kinetic energy of a moving mass is...
Ch. 2.8 - Determine the specific kinetic energy of a mass...Ch. 2.8 - Calculate the total potential energy, in Btu, of...Ch. 2.8 - Determine the specific potential energy, in kJ/kg,...Ch. 2.8 - An object whose mass is 100 kg is located 20 m...Ch. 2.8 - A water jet that leaves a nozzle at 60 m/s at a...Ch. 2.8 - Consider a river flowing toward a lake at an...Ch. 2.8 - At a certain location, wind is blowing steadily at...Ch. 2.8 - What is the caloric theory? When and why was it...Ch. 2.8 - In what forms can energy cross the boundaries of a...Ch. 2.8 - What is an adiabatic process? What is an adiabatic...Ch. 2.8 - When is the energy crossing the boundaries of a...Ch. 2.8 - Consider an automobile traveling at a constant...Ch. 2.8 - A room is heated by an iron that is left plugged...Ch. 2.8 - A room is heated as a result of solar radiation...Ch. 2.8 - A gas in a pistoncylinder device is compressed,...Ch. 2.8 - A small electrical motor produces 5 W of...Ch. 2.8 - A car is accelerated from rest to 85 km/h in 10 s....Ch. 2.8 - A construction crane lifts a prestressed concrete...Ch. 2.8 - Determine the torque applied to the shaft of a car...Ch. 2.8 - A spring whose spring constant is 200 lbf/in has...Ch. 2.8 - How much work, in kJ, can a spring whose spring...Ch. 2.8 - A ski lift has a one-way length of 1 km and a...Ch. 2.8 - The engine of a 1500-kg automobile has a power...Ch. 2.8 - A damaged 1200-kg car is being towed by a truck....Ch. 2.8 - As a spherical ammonia vapor bubble rises in...Ch. 2.8 - A steel rod of 0.5 cm diameter and 10 m length is...Ch. 2.8 - What are the different mechanisms for transferring...Ch. 2.8 - For a cycle, is the net work necessarily zero? For...Ch. 2.8 - On a hot summer day, a student turns his fan on...Ch. 2.8 - Water is being heated in a closed pan on top of a...Ch. 2.8 - An adiabatic closed system is accelerated from 0...Ch. 2.8 - A fan is to accelerate quiescent air to a velocity...Ch. 2.8 - A vertical pistoncylinder device contains water...Ch. 2.8 - At winter design conditions, a house is projected...Ch. 2.8 - A water pump increases the water pressure from 15...Ch. 2.8 - The lighting needs of a storage room are being met...Ch. 2.8 - A university campus has 200 classrooms and 400...Ch. 2.8 - Consider a room that is initially at the outdoor...Ch. 2.8 - An escalator in a shopping center is designed to...Ch. 2.8 - Consider a 2100-kg car cruising at constant speed...Ch. 2.8 - Prob. 51PCh. 2.8 - What is mechanical efficiency? What does a...Ch. 2.8 - How is the combined pumpmotor efficiency of a pump...Ch. 2.8 - Can the combined turbinegenerator efficiency be...Ch. 2.8 - Consider a 2.4-kW hooded electric open burner in...Ch. 2.8 - The steam requirements of a manufacturing facility...Ch. 2.8 - Reconsider Prob. 256E. Using appropriate software,...Ch. 2.8 - A 75-hp (shaft output) motor that has an...Ch. 2.8 - Prob. 59PCh. 2.8 - An exercise room has six weight-lifting machines...Ch. 2.8 - A room is cooled by circulating chilled water...Ch. 2.8 - The water in a large lake is to be used to...Ch. 2.8 - A 7-hp (shaft) pump is used to raise water to an...Ch. 2.8 - A geothermal pump is used to pump brine whose...Ch. 2.8 - At a certain location, wind is blowing steadily at...Ch. 2.8 - Reconsider Prob. 265. Using appropriate software,...Ch. 2.8 - Water is pumped from a lower reservoir to a higher...Ch. 2.8 - An 80-percent-efficient pump with a power input of...Ch. 2.8 - Water is pumped from a lake to a storage tank 15 m...Ch. 2.8 - Large wind turbines with a power capacity of 8 MW...Ch. 2.8 - A hydraulic turbine has 85 m of elevation...Ch. 2.8 - The water behind Hoover Dam in Nevada is 206 m...Ch. 2.8 - An oil pump is drawing 44 kW of electric power...Ch. 2.8 - A wind turbine is rotating at 15 rpm under steady...Ch. 2.8 - How does energy conversion affect the environment?...Ch. 2.8 - What is acid rain? Why is it called a rain? How do...Ch. 2.8 - Why is carbon monoxide a dangerous air pollutant?...Ch. 2.8 - What is the greenhouse effect? How does the excess...Ch. 2.8 - What is smog? What does it consist of? How does...Ch. 2.8 - Consider a household that uses 14,000 kWh of...Ch. 2.8 - When a hydrocarbon fuel is burned, almost all of...Ch. 2.8 - Prob. 82PCh. 2.8 - A typical car driven 20,000 km a year emits to the...Ch. 2.8 - Prob. 84PCh. 2.8 - What are the mechanisms of heat transfer?Ch. 2.8 - Which is a better heat conductor, diamond or...Ch. 2.8 - How does forced convection differ from natural...Ch. 2.8 - What is a blackbody? How do real bodies differ...Ch. 2.8 - Define emissivity and absorptivity. What is...Ch. 2.8 - Does any of the energy of the sun reach the earth...Ch. 2.8 - The inner and outer surfaces of a 5-m 6-m brick...Ch. 2.8 - The inner and outer surfaces of a 0.5-cm-thick 2-m...Ch. 2.8 - Reconsider Prob. 292. Using appropriate software,...Ch. 2.8 - Prob. 94PCh. 2.8 - Prob. 95PCh. 2.8 - Prob. 96PCh. 2.8 - Prob. 97PCh. 2.8 - For heat transfer purposes, a standing man can be...Ch. 2.8 - Prob. 99PCh. 2.8 - Prob. 100PCh. 2.8 - A 1000-W iron is left on the ironing board with...Ch. 2.8 - A 7-cm-external-diameter, 18-m-long hot-water pipe...Ch. 2.8 - A thin metal plate is insulated on the back and...Ch. 2.8 - Reconsider Prob. 2103. Using appropriate software,...Ch. 2.8 - The outer surface of a spacecraft in space has an...Ch. 2.8 - Prob. 106PCh. 2.8 - A hollow spherical iron container whose outer...Ch. 2.8 - Some engineers have developed a device that...Ch. 2.8 - Consider a classroom for 55 students and one...Ch. 2.8 - Consider a homeowner who is replacing his...Ch. 2.8 - Prob. 111RPCh. 2.8 - The U.S. Department of Energy estimates that...Ch. 2.8 - A typical household pays about 1200 a year on...Ch. 2.8 - Prob. 114RPCh. 2.8 - Prob. 115RPCh. 2.8 - Prob. 116RPCh. 2.8 - Consider a TV set that consumes 120 W of electric...Ch. 2.8 - Water is pumped from a 200-ft-deep well into a...Ch. 2.8 - Consider a vertical elevator whose cabin has a...Ch. 2.8 - Prob. 120RPCh. 2.8 - In a hydroelectric power plant, 65 m3/s of water...Ch. 2.8 - The demand for electric power is usually much...Ch. 2.8 - The pump of a water distribution system is powered...Ch. 2.8 - Prob. 124RPCh. 2.8 - A 2-kW electric resistance heater in a room is...Ch. 2.8 - Prob. 126FEPCh. 2.8 - A 75-hp compressor in a facility that operates at...Ch. 2.8 - On a hot summer day, the air in a well-sealed room...Ch. 2.8 - A fan is to accelerate quiescent air to a velocity...Ch. 2.8 - A 900-kg car cruising at a constant speed of 60...Ch. 2.8 - Prob. 131FEPCh. 2.8 - Prob. 132FEPCh. 2.8 - A 2-kW pump is used to pump kerosene ( = 0.820...Ch. 2.8 - Prob. 134FEPCh. 2.8 - Prob. 135FEPCh. 2.8 - Prob. 136FEPCh. 2.8 - Prob. 137FEPCh. 2.8 - Heat is transferred steadily through a...Ch. 2.8 - The roof of an electrically heated house is 7 m...
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