Theory of Machine
The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where δS = Static deflection of simply supported shaft due to uniformly distributed load)

0.571/ √δS
0.4985/ √δS
0.6253/ √δS
0.5615/ √δS

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Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r (cos 2θ/n)
m.ω².r sinθ
m.ω².r cosθ
m.ω².r (sin 2θ/n)

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