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 4.2, Problem 36P
Program Plan Intro
If the particle moves under uniform electric field then show that the trajectory of the will be cycloid.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the solution.
given the following equation
x2 = 16
O a. (+4,-2)
O b. (+2,-4)
O c. No Solution
O d. (+4,-4)
2. 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…
Chapter 4 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.1 - Prob. 4PCh. 4.1 - Prob. 5PCh. 4.1 - Prob. 6PCh. 4.1 - Prob. 7PCh. 4.1 - Prob. 8PCh. 4.1 - Prob. 9PCh. 4.1 - Prob. 10P
Ch. 4.1 - Prob. 11PCh. 4.1 - Prob. 12PCh. 4.1 - Prob. 13PCh. 4.1 - Prob. 14PCh. 4.1 - Prob. 15PCh. 4.1 - Prob. 16PCh. 4.1 - Prob. 17PCh. 4.1 - Prob. 18PCh. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Prob. 21PCh. 4.1 - Prob. 22PCh. 4.1 - Prob. 23PCh. 4.1 - Prob. 24PCh. 4.1 - Prob. 25PCh. 4.1 - Prob. 26PCh. 4.1 - Prob. 27PCh. 4.1 - Prob. 28PCh. 4.1 - Prob. 29PCh. 4.1 - Prob. 30PCh. 4.1 - Prob. 31PCh. 4.1 - Prob. 32PCh. 4.1 - Prob. 33PCh. 4.1 - Repeat Problem 33, except with the generator...Ch. 4.1 - A particle of mass m moves in the plane with...Ch. 4.1 - Prob. 36PCh. 4.1 - Prob. 37PCh. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.2 - Prob. 7PCh. 4.2 - Prob. 8PCh. 4.2 - Prob. 9PCh. 4.2 - Prob. 10PCh. 4.2 - Prob. 11PCh. 4.2 - Prob. 12PCh. 4.2 - Prob. 13PCh. 4.2 - Prob. 14PCh. 4.2 - Prob. 15PCh. 4.2 - Prob. 16PCh. 4.2 - Prob. 17PCh. 4.2 - Prob. 18PCh. 4.2 - Prob. 19PCh. 4.2 - Prob. 20PCh. 4.2 - Suppose that L1=a1D2+b1D+c1 and L2=a2D2+b2D+c2,...Ch. 4.2 - Suppose that L1x=tDx+x and that L2x=Dx+tx. Show...Ch. 4.2 - Prob. 23PCh. 4.2 - Prob. 24PCh. 4.2 - Prob. 25PCh. 4.2 - Prob. 26PCh. 4.2 - Prob. 27PCh. 4.2 - Prob. 28PCh. 4.2 - Prob. 29PCh. 4.2 - Prob. 30PCh. 4.2 - Prob. 31PCh. 4.2 - Prob. 32PCh. 4.2 - Prob. 33PCh. 4.2 - Prob. 34PCh. 4.2 - Prob. 35PCh. 4.2 - Prob. 36PCh. 4.2 - Prob. 37PCh. 4.2 - Prob. 38PCh. 4.2 - Prob. 39PCh. 4.2 - Prob. 40PCh. 4.2 - Prob. 41PCh. 4.2 - Prob. 42PCh. 4.2 - Prob. 43PCh. 4.2 - Prob. 44PCh. 4.2 - Prob. 45PCh. 4.2 - Prob. 46PCh. 4.2 - Prob. 47PCh. 4.2 - Prob. 48PCh. 4.3 - Prob. 1PCh. 4.3 - Prob. 2PCh. 4.3 - Prob. 3PCh. 4.3 - Prob. 4PCh. 4.3 - Prob. 5PCh. 4.3 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10PCh. 4.3 - Prob. 11PCh. 4.3 - Prob. 12PCh. 4.3 - Prob. 13PCh. 4.3 - Prob. 14PCh. 4.3 - Suppose that a projectile is fired straight upward...Ch. 4.3 - Prob. 16PCh. 4.3 - Prob. 17PCh. 4.3 - Prob. 18PCh. 4.3 - Prob. 19PCh. 4.3 - Prob. 20PCh. 4.3 - Suppose that an artillery projectile is fired from...
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
- (Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.arrow_forwardQ1: Consider a surface of revolution generated by a Bezier curve defined by the four control points P(0,0,0), (2,1,2), P₂ (3,3,0) P, (2,2,3) respectively, rotating about the X-axis. Calculate the point on the surface at u = 0.25, 0= π/2.arrow_forwardPlease solve.arrow_forward
- The 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_forward5arrow_forward2. 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):arrow_forward
- A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. Q' (t) = = (b) Find the quantity of salt in the tank as it's about to overflow. esc C ✓ % 1 1 a 2 W S # 3 e d $ 4 f 5 rt 99 6 y & 7 h O u * 00 8 O 1 9 1 Oarrow_forwardWrite a computer program that can be used to determine the magni- Computer Problems 73 tude and direction of the resultant of n forces F;, where i = 1, 2, . . . , n, that are applied at point A, of coordinates x, Yo, and zo, knowing that the line of action of F; passes through point A¡ of coordinates x¡, Yi, and z¡. Az(X2. Y2. Z2) A,(X1. Y1. Z1) F2 Ao(Xo. Yo, Zo) Fn A,(Xp Ym Zn) Fi A,(X; Yp Z.)arrow_forwardQ.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 4arrow_forward
- 4arrow_forwardPlease do it fast give typed answer I will upvotearrow_forwardA baseball is hit such that it travels straight upward after being struck by the bat. A fan observes that it requires 3.00 s for the ball to reach its maximum height. Find (a) its initial velocity and (b) its maximum height. Ignore the effects of air resistance.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_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