The transient vibrations of the drive line developed during the application of a cone (friction) clutch lead to unpleasant noise. To reduce the noise, a flywheel having a mass moment of inertia \(J_{2}\) is attached to the drive line through a torsional spring \(k_{t 2}\) and a viscous torsional damper \(c_{t 2}\), as shown in Fig. 5.63. If the mass moment of inertia of the cone clutch is \(J_{1}\) and the stiffness and damping constant of the drive line are given by \(k_{t 1}\) and \(c_{t 1}\), respectively, derive the relations to be satisfied for the stable operation of the system.

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Prime mover Cone clutch, J Flywheel. J k12 C12 Load Drive line 02 FIGURE 5.63 Driveline connected to cone clutch and flywheel