Differential Equations (with DE Tools Printed Access Card)
4th Edition
ISBN: 9781133109037
Author: Paul Blanchard
Publisher: Cengage Learning
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Chapter 2.3, Problem 10E
In Exercises 9 and 10, we consider a mass sliding on a frictionless table between two walls that are 1 unit apart and connected to both walls with springs, as shown below. 
Let k1, and k2be the spring constants of the left and right spring, respectively, let m be the mass, and let b be the damping coefficient of the medium the spring is sliding through. Suppose L1and L2are the rest lengths of the left and right springs, respectively.
10. (a) Convert the second-order equation of Exercise 9 into a first-order system.
(b) Find the equilibrium point of this system.
(c) Using your result from part (b), pick a new
(d) How does this new system compare o the system for a damped harmonic oscillator?
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Chapter 2 Solutions
Differential Equations (with DE Tools Printed Access Card)
Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Consider the predator-prey system...Ch. 2.1 - Consider the predator-prey system dRdt=2R(1R...Ch. 2.1 - Exercises 9-14 refer to the predator-prey and the...Ch. 2.1 - Exercises 9-14 refer to the predator-prey and the...
Ch. 2.1 - Exercises 9-14 refer to the predator-prey and the...Ch. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Exercises 9-14 refer to the predator-prey and the...Ch. 2.1 - Prob. 15ECh. 2.1 - Consider the system of predator-prey equations...Ch. 2.1 - Pesticides that kill all insect species are not...Ch. 2.1 - Some predator species seldom capture healthy adult...Ch. 2.1 - Prob. 19ECh. 2.1 - Consider the initial-value problem d2ydt2+kmy=0...Ch. 2.1 - A mass weighing 12 pounds stretches a spring 3...Ch. 2.1 - A mass weighing 4 pounds stretches a spring 4...Ch. 2.1 - Do the springs in an “extra firm’ mattress have a...Ch. 2.1 - Consider a vertical mass-spring system as shown in...Ch. 2.1 - Exercises 25—30 refer to a situation in which...Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Exercises 25—30 refer to a situation in which...Ch. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Convert the second-order differential equation 1...Ch. 2.2 - Prob. 9ECh. 2.2 - Consider the system dxdt=2x+ydydt=2y and its...Ch. 2.2 - Eight systems of differential equations and four...Ch. 2.2 - Consider the modified predator-prey system...Ch. 2.2 - In Exercises 13—18. (a) find the equilibrium...Ch. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - In Exercises 13—18. (a) find the equilibrium...Ch. 2.2 - Prob. 17ECh. 2.2 - In Exercises 13—18. (a) find the equilibrium...Ch. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Consider the four solution curves in the phase...Ch. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - Prob. 5ECh. 2.3 - In the damped harmonic oscillator, we assume that...Ch. 2.3 - Consider any damped harmonic oscillator equation...Ch. 2.3 - Consider any damped harmonic oscillator equation...Ch. 2.3 - In Exercises 9 and 10, we consider a mass sliding...Ch. 2.3 - In Exercises 9 and 10, we consider a mass sliding...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - Prob. 6ECh. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - Prob. 8ECh. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Consider the partially decoupled system...Ch. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - In Exercises 3—6, a system, an initial condition,...Ch. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Using a computer or calculator, apply Euler’s...Ch. 2.5 - Prob. 8ECh. 2.6 - Consider the system dxdt=x+ydydt=y (a) Show that...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - (a) Suppose Y1(t) is a solution of an autonomous...Ch. 2.6 - Prob. 9ECh. 2.6 - Consider the system dxdt=2dydt=y2 (a) Calculate...Ch. 2.6 - Consider the system dxdt=2dydt=y2 Show that, for...Ch. 2.7 - Prob. 1ECh. 2.7 - In the SIR model, we assume that everyone in the...Ch. 2.7 - Vaccines make it possible to prevent epidemics....Ch. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - One of the basic assumptions of the SIR model is...Ch. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - Using =1.66 and the value of that you determined...Ch. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2 - Prob. 1RECh. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - In Exercises 31-34, a solution curve in the...Ch. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Consider the partially decoupled system...Ch. 2 - Consider the partially decoupled system...Ch. 2 - Prob. 37RE
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