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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Question
could you please provide explanations
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2F1016526c-2046-43b2-a586-2024bd3d8d90%2F3101f2s_processed.png&w=3840&q=75)
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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