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Two homogeneous spheres of mass M radius R joined by a bar of length L, negligible mass, and suspended from their geometric center by a string 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 I is the moment of inertia of a sphere with respect to the vertical axis that passes through the wire, determine the damping factor and natural frequency. (image 2)

Two homogeneous spheres of mass M radius R joined by a bar of length L, negligible mass, and suspended from their geometric center by a string 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 I is the moment of inertia of a sphere with respect to the vertical axis that passes through the wire, determine the damping factor and natural frequency. (image 2)

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, negligible mass, and suspended from their geometric center by a string 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 I is the moment of inertia of a sphere with respect to the vertical axis that passes through the wire, determine the damping factor and natural frequency. (image 2)

3πη (L k a.시 = +R) R & wo I 2 21 +R b.거= & wo = 21 3πη C.거= I L +R 2 & wo = Vī 2 2 +R |k wo = I d. Y= . 거= & I k 3πη L I 2 e.거= wo = 21 2.
Transcribed Image Text:3πη (L k a.시 = +R) R & wo I 2 21 +R b.거= & wo = 21 3πη C.거= I L +R 2 & wo = Vī 2 2 +R |k wo = I d. Y= . 거= & I k 3πη L I 2 e.거= wo = 21 2.
M M
Transcribed Image Text:M M
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