Q 3. A solid shaft having diameter d = 8 cm, length I = 35 cm and modulus of rigidity G = 4 x 1010 N/m2 is attached to a circular disc which has mass moment of inertin / = 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 (iv) The torsional damning cocfficient cof the system

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Q3.
A solid shaft having diameter d = 8 cm, length I= 35 cm and modulus of
rigidity G = 4 x 1010 N/m? is attached to a circular disc which has mass moment of
inertia / = 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
(iv) The torsional damping coefficient cof the system
(iv) The time period for damped vibration
Transcribed Image Text:Q3. A solid shaft having diameter d = 8 cm, length I= 35 cm and modulus of rigidity G = 4 x 1010 N/m? is attached to a circular disc which has mass moment of inertia / = 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 (iv) The torsional damping coefficient cof the system (iv) The time period for damped vibration
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