An inelastic rod OM, with length 1 And its mass is neglected, carrying at the end a particle of mass m «The rod can rotate freely in the vertical plane ( xOz ) around ( Oy ) at fixed point O. The rod is pushed away from its equilibrium position ( 0 = 0 ) as the figue showin , In addition to the force of gravity g and the tensile force T of the rod . A particle is subjected to frictional force F Proportional to its velocity V. (f=- µV). The Question is : If we assume that the angle of displacement is small ( sin 0 ×0 ) and that the coefficient of friction ( u = 0 ) show that the differential equation is ( Ö + w² 0 = 0 ) then deduce w. and what is the type of the motion in this case ?
An inelastic rod OM, with length 1 And its mass is neglected, carrying at the end a particle of mass m «The rod can rotate freely in the vertical plane ( xOz ) around ( Oy ) at fixed point O. The rod is pushed away from its equilibrium position ( 0 = 0 ) as the figue showin , In addition to the force of gravity g and the tensile force T of the rod . A particle is subjected to frictional force F Proportional to its velocity V. (f=- µV). The Question is : If we assume that the angle of displacement is small ( sin 0 ×0 ) and that the coefficient of friction ( u = 0 ) show that the differential equation is ( Ö + w² 0 = 0 ) then deduce w. and what is the type of the motion in this case ?
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![An inelastic rod OM, with length 1 And its mass is neglected, carrying at the end a particle of
mass m «The rod can rotate freely in the vertical plane ( xOz ) around ( Oy ) at fixed point O.
The rod is pushed away from its equilibrium position ( 0 = 0) as the figue showin , In addition to
the force of gravity g and the tensile force T of the rod . A particle is subjected to frictional force
F Proportional to its velocity V. (f=- µV).
The Question is :
If we assume that the angle of displacement is small ( sin 0 = 0 ) and that the coefficient of
friction ( u = 0 ) show that the differential equation is ( Ô + w² 0 = 0 ) then deduce w. and
what is the type of the motion in this case ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2d95e6-5b5d-4432-9c44-ab312d4d7e4f%2F496dd6ff-59a0-473a-af81-6c6b1af93d7c%2F50q1umb_processed.png&w=3840&q=75)
Transcribed Image Text:An inelastic rod OM, with length 1 And its mass is neglected, carrying at the end a particle of
mass m «The rod can rotate freely in the vertical plane ( xOz ) around ( Oy ) at fixed point O.
The rod is pushed away from its equilibrium position ( 0 = 0) as the figue showin , In addition to
the force of gravity g and the tensile force T of the rod . A particle is subjected to frictional force
F Proportional to its velocity V. (f=- µV).
The Question is :
If we assume that the angle of displacement is small ( sin 0 = 0 ) and that the coefficient of
friction ( u = 0 ) show that the differential equation is ( Ô + w² 0 = 0 ) then deduce w. and
what is the type of the motion in this case ?
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