Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 6.2, Problem 3P
Program Plan Intro
Write a code to show the type of critical point is asymptotically stable or unstable.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Q.4 In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth
plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these
temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil does not
vary perceptibly in this temperature range. Consider four experiments at steady state under different
experimental conditions, as shown in the figure Q1. The figure shows plate temperatures and the heat
fluxes in the vertical direction. What is the steady state heat flux (in W m) with the top plate at 90°C and
the bottom plate at 45°C?
[4]
30°C
70°C
40°C
90°C
flux = 39 Wm-2
flux =30 Wm2
flux = 52 Wm 2
flux ? Wm-2
60°C
35°C
80°C
45°C
Experiment 1
Experiment 2
Experiment 3
Experiment 4
2. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):
For an object of mass m=3 kg to slide without friction up the rise of height h=1 m shown, it must have a
minimum initial kinetic energy (in J) of:
h
O a. 40
O b. 20
O c. 30
O d. 10
Chapter 6 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 6.1 - Prob. 1PCh. 6.1 - Prob. 2PCh. 6.1 - Prob. 3PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10P
Ch. 6.1 - Prob. 11PCh. 6.1 - Prob. 12PCh. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.1 - Prob. 15PCh. 6.1 - Prob. 16PCh. 6.1 - Prob. 17PCh. 6.1 - Prob. 18PCh. 6.1 - Prob. 19PCh. 6.1 - Prob. 20PCh. 6.1 - Prob. 21PCh. 6.1 - Prob. 22PCh. 6.1 - Prob. 23PCh. 6.1 - Prob. 24PCh. 6.1 - Prob. 25PCh. 6.1 - Prob. 26PCh. 6.1 - Prob. 27PCh. 6.1 - Prob. 28PCh. 6.1 - Prob. 29PCh. 6.1 - Prob. 30PCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.2 - Prob. 3PCh. 6.2 - Prob. 4PCh. 6.2 - Prob. 5PCh. 6.2 - Prob. 6PCh. 6.2 - Prob. 7PCh. 6.2 - Prob. 8PCh. 6.2 - Prob. 9PCh. 6.2 - Prob. 10PCh. 6.2 - Prob. 11PCh. 6.2 - Prob. 12PCh. 6.2 - Prob. 13PCh. 6.2 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - Prob. 21PCh. 6.2 - Prob. 22PCh. 6.2 - Prob. 23PCh. 6.2 - Prob. 24PCh. 6.2 - Prob. 25PCh. 6.2 - Prob. 26PCh. 6.2 - Prob. 27PCh. 6.2 - Prob. 28PCh. 6.2 - Prob. 29PCh. 6.2 - Prob. 30PCh. 6.2 - Prob. 31PCh. 6.2 - Prob. 32PCh. 6.2 - Prob. 33PCh. 6.2 - Prob. 34PCh. 6.2 - Prob. 35PCh. 6.2 - Prob. 36PCh. 6.2 - Prob. 37PCh. 6.2 - Prob. 38PCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.3 - Prob. 3PCh. 6.3 - Prob. 4PCh. 6.3 - Prob. 5PCh. 6.3 - Prob. 6PCh. 6.3 - Prob. 7PCh. 6.3 - Problems 8 through 10 deal with the competition...Ch. 6.3 - Problems 8 through 10 deal with the competition...Ch. 6.3 - Problems 8 through 10 deal with the competition...Ch. 6.3 - Prob. 11PCh. 6.3 - Prob. 12PCh. 6.3 - Prob. 13PCh. 6.3 - Prob. 14PCh. 6.3 - Prob. 15PCh. 6.3 - Prob. 16PCh. 6.3 - Prob. 17PCh. 6.3 - Prob. 18PCh. 6.3 - Prob. 19PCh. 6.3 - Prob. 20PCh. 6.3 - Prob. 21PCh. 6.3 - Prob. 22PCh. 6.3 - Prob. 23PCh. 6.3 - Prob. 24PCh. 6.3 - Prob. 25PCh. 6.3 - Prob. 26PCh. 6.3 - Prob. 27PCh. 6.3 - Prob. 28PCh. 6.3 - Prob. 29PCh. 6.3 - Prob. 30PCh. 6.3 - Prob. 31PCh. 6.3 - Prob. 32PCh. 6.3 - Prob. 33PCh. 6.3 - Prob. 34PCh. 6.4 - Prob. 1PCh. 6.4 - Prob. 2PCh. 6.4 - Prob. 3PCh. 6.4 - Prob. 4PCh. 6.4 - Prob. 5PCh. 6.4 - Prob. 6PCh. 6.4 - Prob. 7PCh. 6.4 - Prob. 8PCh. 6.4 - Prob. 9PCh. 6.4 - Prob. 10PCh. 6.4 - Prob. 11PCh. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.4 - Prob. 14PCh. 6.4 - Prob. 15PCh. 6.4 - Prob. 16PCh. 6.4 - Prob. 17PCh. 6.4 - Prob. 18PCh. 6.4 - Prob. 19PCh. 6.4 - Prob. 20PCh. 6.4 - Prob. 21PCh. 6.4 - Prob. 22PCh. 6.4 - Prob. 23PCh. 6.4 - Prob. 24PCh. 6.4 - Prob. 25PCh. 6.4 - Prob. 26P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- b. Consider the system below described by state and output equations of the state space model * = (, )x+ (-)u; y For this system, prove that it is POSSIBLE to determine the controllability but IMPOSSIBLE to determine the observability.arrow_forwardSolve the following equations. Be sure to check the potential solution(s) in the original equation, to see whether it (they) are in the domain. (a) log, (r? –x – 2) = 2arrow_forward2. The Lorenz equations originating from models of atmospheric physics are given as follows: dr = 10 (y - 2) dt (2a) %3D dy 28r – y -rz (2b) dt dz ay - 2.6666672 (2c) dt with initial conditions r(0) = y(0) = 2(0) = 5. (a) Evaluate the eigenvalues of the Jacobian matrix at t = 0. Is the problem stiff? Estimate the maximum time step that can be selected to keep the solution stable when the fourth-order Runge-Kutta method is used. (b) Solve the given system to t = 50 using the fourth-order Runge-Kutta method. Set the time step to 0.1. Plot the solution. All three functions (2(t), y(t), z(t)) should be present on one plot. • Set the time step to 10 3 and 10 6. Plot r(t) obtained at the three time steps (the first one is 0.1 from above) on one plot. Describe the behaviour. How does the value of the time step affect the result? Set the time step to 10-6 and use the initial conditions r(0) = y(0) = 5.0 and 2(0) = 5.00001. Plot z(t) obtained at the two different sets of initial conditions on…arrow_forward
- 7. A system is stable if all its roots of the characteristic equation are (a) positive (b) negative (d) any of the abovearrow_forwardgiven the following equation x2 = 16 O a. (+4,-2) O b. (+2,-4) O c. No Solution O d. (+4,-4)arrow_forwardSuppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.arrow_forward
- 3. Consider the following nonlinear system of 2 equations with 2 unknowns: x² + 4y? = 1 2² + (y – 1)² = 1 (a) By hand: sketch the two curves in the ry-plane, and find all solutions by doing some basic algebra. (b) By hand: apply two steps of Newton's multivariate method to approximate one of the solutions of the system above starting from (1, 1). (c) Use NewtonMD Maple/Python file to find one of the numerical solution for the above system with six correct decimal places starting from (1.0, 1.0).arrow_forwardThe following is used to model a wave that impacts a concrete wall created by the US Navy speed boat.1. Derive the complete piecewise function of F(t) and F()The concrete wall is 2.8 m long with a cross-section area of 0.05 m2. The force at time equal zero is 200 N. It is also known that the mass is modeled as lumped at the end of 1200 kg and Young’s modulus of 3.6 GPa2. Use *Matlab to simulate and plot the total response of the system at zero initial conditions and t0 = 0.5 sarrow_forwardUse the dsolve() function to solve the differential equation 8Dy3(t) = cos(20t) + sin(2t) for initial conditions y(10) = 50, Dy(0) = 0, Dy2(0) = 0, and y(10) = 5, Dy(0) = 0, Dy2(0) = 3. Plot your solutions on a single figure as a solid curve for the first set initial conditions and a dotted curve fo rthe second set of initial conditions for time t = -10 to 20. Make sureu to label both axes and title your figure, and turn on the plotting legend. Set teh y-axis limits to [-150 200].arrow_forward
- Problem 1 The position x as a function of time of a particle that moves along a straight line is given by: r(1) = (-3 + 41)c 0. f1 0.1t The velocity v(t) of the particle is determined by the derivative of r(t) with respect to t, and the accelerationa(t) is determined by the derivative ofv(t) with respect to t. Derive the expressions for the velocity and acceleration of the particle, and make plots of the position, velocity, and acceleration as functions of time for0arrow_forwardPlease solve.arrow_forwardSITUATION 1 (Fluid Flow in a Closed Conduit) Consider a fluid, with density (p) of 998.21 kg/m³ and dynamic viscosity (u) of 1.002 x 103 N-s/m², flowing in a 2000-meter long, 50-mm diameter smooth round pipe with velocity of 2.5 m/s. The energy loss on the pipe flow (he) due to friction between the pipe and the fluid is determined using Darcy-Weisbach equation, given as h₁ = f (²) (1/1) where f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of the flow, and g is the gravitational acceleration. The friction factor may be determined using an empirical equation developed by Nikuradse for flow in smooth pipes, given as 1 =0.869 In (Re√7)-0.8 where Re is the Reynolds number of the flow, determined as VDp R₂ = μl The friction factor equation given is only valid for flows with Reynolds number higher than 4000 (turbulent flow). Guide Questions: Determine the Reynolds number of the flow. Is the Nikuradse equation for friction factor…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
C++ for Engineers and Scientists
Computer Science
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Course Technology Ptr
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole