Problem 4 critical speeds of shaft, Dunkerley's method, natural frequency free transverse vibration

Solve 1 problem on Dunkerley's method A shaft 1.5 m long, supported in flexible bearings at the end carries two wheels each of 50 kg mass. One wheel is situated at the centre of the shaft and other at a distance of 375 mm from the centre towards left. The shaft is hollow of external diameter 75 mm and internal diameter 40 mm. The density of material is 7700 kg/m^3 and it's modulus of elasticity is 200 GN/m^2. Find the lowest whirling speed of the shaft, taking into account the mass of shaft. 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...