Problem 3 on critical speeds of shaft, damped vertical shaft with single rotor

Solve Problem on damped vertical shaft with single rotor. A horizontal shaft of 10 mm diameter is simply supported at both ends by bearings. A rotor of mass 5 kg is attached at middle of the horizontal shaft. The span between two bearings is 500 mm. The centre gravity of rotor is 2.5 mm offset from geometric centre of the rotor. The equivalent viscous damping at the centre of rotor shaft may be taken as 52 Ns/m . Find the deflection of the shaft and critical speed of the shaft. Assume E= 200×10^9 N/m^2 speed of the shaft= 720 rpm Please refer my following Playlists , Links are given: 1. Theory of Machines or Kinematics of Machines play list    • Theory Of Machines playlist   2. Fluid mechanics and Hydraulic machines playlist    • Fluid mechanics and hydraulic machines   3. Refrigeration and air conditioning playlist    • Refrigeration and air conditioning   4. Renewable Energy engineering or Non-convensional energy sources play list    • Renewable energy engineering/ Non-conventi...   5. Dynamics of Machinery play list    • Dynamics of machinery / Mechanical Vibrati...   6. Engineering graphics or Engineering drawing play list    • Engineering Graphics Playlist   7. Engineering Mechanics Playlist    • Engineering Mechanics Playlist   8. Power plant engineering play list    • Power Plant Engineering( Mechanical Branch...   9. Engineering Thermodynamics play list    • Thermodynamics / Thermal Engineering   Pla...   10. Heat and mass transfer play list    • Heat and Mass Transfer Playlist   11. Operation research play list    • Operation Research Playlist   12. Strength of material playlist    • Strength Of Materials Play list   13. Control Engineering/ Control systems engineering playlist    • Control Systems playlist ( EnTC & Mechanic...