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Theory of Machine

Theory of Machine
If ‘D₁’ and ‘D₂’ be the diameters of driver and driven pulleys, then belt speed is proportional to

D₁
D₁.D₂
D₂/D₁
D₁/D₂

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Theory of Machine
A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by (where μ = tan φ = Coefficient of friction between the plane and the body)

P = W tan (α + φ)
P = W (sin α + μ cos α)
P = W tan α
P = W (cos α + μ sin α)

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Theory of Machine
A point on a link connecting double slider crank chain traces a

Hyperbola
Ellipse
Circle
Parabola

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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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Theory of Machine
The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft, and I = Mass moment of inertia of the disc attached at the end of a shaft)

2π. √(q/I)
1/2π
2π qI
(1/2π). √(q/I)

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Theory of Machine
The fundamental equation for correct steering is (where φ and α = Angle through which the axis of the outer wheel and inner wheel turns respectively, c = Distance between the pivots of the front axles, and d = Wheel base)

tanφ + cotα = b/c
sinφ + sinα = b/c
cotφ - cotα = c/b
cosφ - sinα = c/b

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