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Theory of Machine

Theory of Machine
The critical speed of a shaft depends upon its

Stiffness and eccentricity
Mass and stiffness
Mass
Stiffness

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Theory of Machine
The driving and driven shafts connected by a Hooke's joint will have equal speeds, if

cotθ = cosα
tanθ = ± cosα
cosθ = sinα
sinθ = ± tanα

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Theory of Machine
The velocity of the belt for maximum power is (where m = Mass of the belt in kg per meter length)

(T.g)/3
√(3m/T)
T/3
√(T/3m)

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Theory of Machine
The maximum efficiency of spiral gears is (where θ = Shaft angle, and φ = Friction angle)

sin (θ + φ) + 1/ cos (θ - φ) + 1
cos (θ - φ) + 1/ sin (θ + φ) + 1
cos (θ + φ) + 1/ cos (θ - φ) + 1
cos (θ - φ) + 1/ cos (θ + φ) + 1

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Theory of Machine
In a reciprocating steam engine, when the crank has turned from inner dead centre through an angle θ, the angular velocity of the connecting rod is given by

ω cosθ/(n² - sin²θ)1/2
ω sinθ/(n² - sin²θ)1/2
ω cosθ/(n² - cos²θ)1/2
ω sinθ/(n² - cos²θ)1/2

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Theory of Machine
The equation of motion for a single degree of freedom system with viscous damping is 4(dx²/dt²) + 9(dx/dt) + 16x. The damping ratio of the system is

44082
44090
30195
9/128

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