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Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Two homogeneous spheres of mass M radius R joined by a bar of length L = 2R, negligible mass, and suspended from its geometric center by a rope such that when rotated ϕ exerts torque −kϕ with k torsion coefficient of the wire. The air exerts dissipative effect F = −6πηv on each sphere, where η is the viscosity of the air and v is the linear velocity of each sphere. If I0 = 25MR2 is the moment of inertia of a sphere with respect to its center of mass (image 1)

determine the equation of motion of the pendulum. (image 2)

M M
Transcribed Image Text:M M
10 6πη dφ 5 k + 44 MR? $ = 0 а. dt? 11 M dt 5 6πη dφ d²o b. dt? k $ = 0 5 + 44 M dt 44 MR? 5 6T7 do + 11 М dt 5 k + 22 MR? с. dt? 0 = 0 d. dt2 5 6πη dφ + 22 M dt 5 + 22 MR? k $ = 0 10 6тп dф 5 k 0 = 0 е. dt? 11 M dt 22 MR2
Transcribed Image Text:10 6πη dφ 5 k + 44 MR? $ = 0 а. dt? 11 M dt 5 6πη dφ d²o b. dt? k $ = 0 5 + 44 M dt 44 MR? 5 6T7 do + 11 М dt 5 k + 22 MR? с. dt? 0 = 0 d. dt2 5 6πη dφ + 22 M dt 5 + 22 MR? k $ = 0 10 6тп dф 5 k 0 = 0 е. dt? 11 M dt 22 MR2
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