Calculate the natural frequency of a shaft - Dunkerley's method

Calculate the natural frequency of a shaft according Dunkerley's method

Total length of the shaft	?	mm

Deflection caused by F1	?	mm
Deflection caused by F2	?	mm
Deflection caused by F3	?	mm
Deflection caused by F4	?	mm
Deflection caused by F5	?	mm
Deflection caused by F6	?	mm
Deflection caused by the own weight of the shaft	?	mm

Frequency associated with the deflection caused by F1	?	Hz
Frequency associated with the deflection caused by F2	?	Hz
Frequency associated with the deflection caused by F3	?	Hz
Frequency associated with the deflection caused by F4	?	Hz
Frequency associated with the deflection caused by F5	?	Hz
Frequency associated with the deflection caused by F6	?	Hz
Frequency associated with the deflection caused by the own weight of the shaft	?	Hz

Natural frequency f_n	?	Hz
Critical speed associated with the natural frequency f_n	?	RPM

Point load F1		N
Point load F2		N
Point load F3		N
Point load F4		N
Point load F5		N
Point load F6		N
Distance a₁		mm
Distance a₂		mm
Distance a₃		mm
Distance a₄		mm
Distance a₅		mm
Distance a₆		mm
Distance a₇		mm
Diameter of the shaft		mm
Elastic modulus of the shaft material		N/mm²
Density of the shaft material		kg/m³

Natural frequency of a shaft according Dunkerley