Theory of Machine
The natural frequency of free longitudinal vibrations is equal to (where m = Mass of the body, s = Stiffness of the body, and δ = Static deflection of the body)

0.4985/√δ
1/2π × √(s/m)
Any one of the listed here
1/2π × √(g/δ)

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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 cosθ
m.ω².r (sin 2θ/n)
m.ω².r sinθ

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