A solid shaft having diameter d = 8 cm, length l = 35 cm and modulus of rigidity G = 4 x 1010 N/m² is attached to a circular disc which has mass moment of inertia J = 0.6 Kg m². If this system is allowed to vibrate in a viscous medium, and the amplitudes of vibratory motion on one side of the mean position for consecutive cycles are found to be 8°,5°, and 3° respectively; Determine the following: (i) The logarithmic decrement, 8 (ii) The damping ratio, } (iii) The torsional stiffness of the solid shaft

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Subject: mom and vibrations
A solid shaft having diameter d = 8 cm, length l = 35 cm and modulus of
rigidity G = 4 x 1010 N/m2 is attached to a circular disc which has mass moment of
inertia J = 0.6 Kg m². If this system is allowed to vibrate in a viscous medium, and the
amplitudes of vibratory motion on one side of the mean position for consecutive cycles are found
to be 8°,5°, and 3° respectively;
Determine the following:
(i) The logarithmic decrement, 8
(ii) The damping ratio, }
(iii) The torsional stiffiness of the solid shaft
(iv) The torsional damping coefficient c of the system
(iv) The time period for damped vibration
Transcribed Image Text:A solid shaft having diameter d = 8 cm, length l = 35 cm and modulus of rigidity G = 4 x 1010 N/m2 is attached to a circular disc which has mass moment of inertia J = 0.6 Kg m². If this system is allowed to vibrate in a viscous medium, and the amplitudes of vibratory motion on one side of the mean position for consecutive cycles are found to be 8°,5°, and 3° respectively; Determine the following: (i) The logarithmic decrement, 8 (ii) The damping ratio, } (iii) The torsional stiffiness of the solid shaft (iv) The torsional damping coefficient c of the system (iv) The time period for damped vibration
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