Consider a particle moving along the x-axis whose motion is modeled by the differential equation given dv by +v =x sin(21) and * dx = v where v is in m/s, x is in meters and t is in seconds. If dt x = 0, v = 4 m's, whent = 0, use Euler's method to determine the approximate value of v and x from t = 0 to t = 25 s using a step size of 0.5 s. (1) Show the first two steps of your solution (set your caleulator in radian). (ii) Then use spreadsheet to complete the table below: t (s) v (m/s) | x(m) 4 0.5 1.0 25
Consider a particle moving along the x-axis whose motion is modeled by the differential equation given dv by +v =x sin(21) and * dx = v where v is in m/s, x is in meters and t is in seconds. If dt x = 0, v = 4 m's, whent = 0, use Euler's method to determine the approximate value of v and x from t = 0 to t = 25 s using a step size of 0.5 s. (1) Show the first two steps of your solution (set your caleulator in radian). (ii) Then use spreadsheet to complete the table below: t (s) v (m/s) | x(m) 4 0.5 1.0 25
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:Consider a particle moving along the x-axis whose motion is modeled by the differential equation given
dv
by
dx
dt
+v =x sin(2r) and
dt
- = v where v is in m/s, x is in meters and t is in seconds. If
x = 0, v = 4 m's, when t = 0, use Euler's method to determine the approximate value of v and x from t = 0
to t = 25 s using a step size of 0.5 s.
%3D
(i) Show the first two steps of your solution (set your calculator in radian).
(ii) Then use spreadsheet to complete the table below:
t (s)
v (m/s) x(m)
4
0.5
1.0
25
(iii) Plot a graph of v and x as functions of t using the same set of coordinates. Choose smooth
from the chart options.
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