Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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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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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