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...

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)

Extracted text: M M


Extracted 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