J.=4 kg-m TO 0000 J =6 kg-m' J.4 kg-m' K K = 1 N-m/rad = 1 N-m/rad D = 1 N-m-s/rad Viscous fluid D =1 N-m-s/rad J -6 kg-m' Pulley (a) Houdaille damper (untuned viscous (b) Model of Houdaille damper system damper) Figure 2: Houdaille damper and model.direction of direction of direction of rotation rotation rotation Te(s ) J .s'O.(s)=0 Jas'Oils) = 0 O KO,(s) J. "KO (s) KO. (s) KO (s) DO, (s) Dse. (s) DO (s) DSO(s) (a) Free-body diagram for "massless" point at the (b) Free-body diagram for the pulley (c) Free-body diagram for the damper head of the crankshaft Figure 4: Free-body diagrams for Houdaille damper from Fig. 2. Determine the equations of motion for the Houdaille damper shown in Fig. 2 with the given model constants.T OOO0 J - 10 kg-m' P 10 kg-m' K K - I N-m/rad -1 N-m/rad Pulley (a) Crankshaft with pulley (b) Model of crankshaft with pulley system