A disk of massm and radius R rolls without slip while restrained by a dashpot with coefficient of viscous damping c in parallel with a spring of stiffness k, as shown in Fig. 2.22. Derive the differential equation for the displacement x(t) of the disk mass center C and determine the viscous damping factor ( and the frequency Wn of undamped oscillation. x(t) k R ww

Elements Of Electromagnetics
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2.19. A disk of mass m and radius R rolls without slip while restrained by a dashpot with coefficient
of viscous damping c in parallel with a spring of stiffness k, as shown in Fig. 2.22. Derive
the differential equation for the displacement x(t) of the disk mass center C and determine
the viscous damping factor C and the frequency wn of undamped oscillation.
x (t)
k
R
ww
C
FIGURE 2.22
Rolling disk restrained by a spring and a dashpot
Transcribed Image Text:2.19. A disk of mass m and radius R rolls without slip while restrained by a dashpot with coefficient of viscous damping c in parallel with a spring of stiffness k, as shown in Fig. 2.22. Derive the differential equation for the displacement x(t) of the disk mass center C and determine the viscous damping factor C and the frequency wn of undamped oscillation. x (t) k R ww C FIGURE 2.22 Rolling disk restrained by a spring and a dashpot
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