6) The system, shown below, hangs in the vertical plane. The bar and the sphere have equal masses m=2-kg, and the moment of inertia of the attached sphere about its own center of mass is assumed negligible. The natural frequency for this system is 2-Hz and the ratio of critical damping is =0.6. The bar is in the vertical position when it is given a counterclockwise angular velocity of 3-rad/s at t= 0-s. Mass m L12 L/2

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6) The system, shown below, hangs in the vertical plane. The bar and the sphere
have equal masses m=2-kg, and the moment of inertia of the attached sphere
about its own center of mass is assumed negligible. The natural frequency for
this system is 2-Hz and the ratio of critical damping is (=0.6. The bar is in the
vertical position when it is given a counterclockwise angular velocity of 3-rad/s
at t= 0-s.
Mass m
L/2
LI2
m
(a) Determine the values of the length L and damping constant C.
(b) At what instant =h does the rotation first attain a maximum value? What is
the corresponding value of (0) at the instant of time 1?
(c) Suppose an electromagnet fastening the sphere to the bar is turned off at r=
causing the sphere to fall away. Derive an expression for 0 a function of time
when =t1.
Transcribed Image Text:6) The system, shown below, hangs in the vertical plane. The bar and the sphere have equal masses m=2-kg, and the moment of inertia of the attached sphere about its own center of mass is assumed negligible. The natural frequency for this system is 2-Hz and the ratio of critical damping is (=0.6. The bar is in the vertical position when it is given a counterclockwise angular velocity of 3-rad/s at t= 0-s. Mass m L/2 LI2 m (a) Determine the values of the length L and damping constant C. (b) At what instant =h does the rotation first attain a maximum value? What is the corresponding value of (0) at the instant of time 1? (c) Suppose an electromagnet fastening the sphere to the bar is turned off at r= causing the sphere to fall away. Derive an expression for 0 a function of time when =t1.
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