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Theory of Machine

Theory of Machine
The Hooke's joint consists of:

Three forks
Four forks
Two forks
One fork

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Theory of Machine
One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where δ = Deflection of the spring)

1/2π. √(δ/g)
2π. √(δ/g)
2π. √(g/δ)
1/2π. √(g/δ)

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Theory of Machine
The acceleration of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by

ω². (r₁ - r₂). (1 - sin² θ)
ω². (r₁ + r₂). [(2 - cos² θ)/cos³ θ]
ω². (r₁ + r₂). (1 + cos² θ)
ω². (r₁ r₂). (1 - cos² θ)

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Theory of Machine
The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where δ = Static deflection of a simply supported shaft due to the point load)

0.5615/√δ
0.6253/√δ
0.4985/√δ
0.571/√δ

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Theory of Machine
The tractive force in a locomotive with two cylinders is given by (where c = Fraction of reciprocating parts per cylinder, m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, and θ = Angle of inclination of crank to the line of stroke)

m.ω².r cosθ
m.ω².r (cosθ - sinθ)
m.ω².r sinθ
(1 - c).m.ω².r (cosθ - sinθ)

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Theory of Machine
In a Hartnell governor, the lift of the sleeve is given by (where r₁ and r₂ = Max. and min. radii of rotation, x = Length of ball arm of the lever, and y = Length of sleeve arm of the lever)

(r₁ - r₂) (y/x)
(r₁ - r₂) (x/y)
(r₁ + r₂) (y/x)
(r₁ + r₂) (x/y)

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