The system shown in Fig. 2.120 has a natural frequency of \(5 \mathrm{~Hz}\) for the following data: \(m=10 \mathrm{~kg}, J_{0}=5 \mathrm{~kg}-\mathrm{m}^{2}, r_{1}=10 \mathrm{~cm}, r_{2}=25 \mathrm{~cm}\). When the system is disturbed by giving it an initial displacement, the amplitude of free vibration is reduced by \(80 \%\) in 10 cycles. Determine the values of \(k\) and \(c\).

Transcribed Image Text:

m -x(t) 0000 k Pulley, mass moment of inertia Jo FIGURE 2.120 System with pulley, dashpot and spring.