This force obeys the following Ordinary Differential Equation: =xF with F(0)=1. Approximate the amount of work, W, done on the object between point 0 and 1.2. dF dx *Use the relationship between work and force: W = F(x) dx *Units of force are in Newtons (abbrev N) and units of work done are Newton-meters (abb Nm) Approximate the solution, F(x), to the given O.D.E using Euler's Method. Specially, fill in the following table. Use Euler's Method x(distance) 0.0 0.3 0.6 0.9 1.2 F(x) (force) 1.000 F_1 F_2 F_3 F_4 Use a step size of 0.3 to compute the four unknown values F_1,F_2,F_3,F_4. Show all work please.
This force obeys the following Ordinary Differential Equation: =xF with F(0)=1. Approximate the amount of work, W, done on the object between point 0 and 1.2. dF dx *Use the relationship between work and force: W = F(x) dx *Units of force are in Newtons (abbrev N) and units of work done are Newton-meters (abb Nm) Approximate the solution, F(x), to the given O.D.E using Euler's Method. Specially, fill in the following table. Use Euler's Method x(distance) 0.0 0.3 0.6 0.9 1.2 F(x) (force) 1.000 F_1 F_2 F_3 F_4 Use a step size of 0.3 to compute the four unknown values F_1,F_2,F_3,F_4. Show all work please.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:dF
dx
This force obeys the following Ordinary Differential Equation: =xF with F(0)=1. Approximate the
amount of work, W, done on the object between point 0 and 1.2.
*Use the relationship between work and force: W = F(x) dx
*Units of force are in Newtons (abbrev N) and units of work done are Newton-meters (abb Nm)
Approximate the solution, F(x), to the given O.D.E using Euler's Method. Specially, fill in the following
table.
Use Euler's Method
x(distance)
0.0
0.3
0.6
0.9
1.2
F(x) (force)
1.000
F_1
F_2
F 3
F 4
Use a step size of 0.3 to compute the four unknown values F_1,F_2,F_3,F_4. Show all work please.
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