For each case, your answer should include: a classification of the stationary point, if required, a determination of any eigenvectors, • an illustration of the trajectories of solutions in the phase plane. Note: It is not required that you solve the system.
For each case, your answer should include: a classification of the stationary point, if required, a determination of any eigenvectors, • an illustration of the trajectories of solutions in the phase plane. Note: It is not required that you solve the system.
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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Question
could you please provide explanations
Transcribed Image Text:The small-amplitude oscillation of a pendulum with angle (t) from the vertical is
modelled using
d²0
dt²
= -0-2k
de
dt'
where k> 0 is a positive coefficient of friction. Let u(t) = 0(t) and v(t) = d0/dt.
Sketch, with supportive calculations, the two possible forms of the phase portrait
in the u-v plane, depending on whether 0 <k <k or k > k, where k is a critical
value to be determined.
For each case, your answer should include:
a classification of the stationary point,
if required, a determination of any eigenvectors,
• an illustration of the trajectories of solutions in the phase plane.
Note: It is not required that you solve the system.
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