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)

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

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Theory of Machine
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of a cross belt drive. The length of the belt is

π (r₁ - r₂) + [(r₁ - r₂)²/x] + 2x
π (r₁ + r₂) + [(r₁ + r₂)²/x] + 2x
π (r₁ - r₂) + [(r₁ + r₂)²/x] + 2x
π (r₁ + r₂) + [(r₁ - r₂)²/x] + 2x

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