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Theory of Machine

Theory of Machine
The equation of free vibrations of a system is (d²x/dt²) +36 π²x, its natural frequency is

3π Hz
6 Hz
6π Hz
3 Hz

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Theory of Machine
To connect two parallel and coplanar shafts the following type of gearing is used

Spiral gear
None of the listed here
Bevel gear
Spur gear

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Theory of Machine
The critical speed of a shaft in revolution per second is __________ as that of natural frequency of transverse vibration.

Different
None of these
Unpredictable
Same

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Theory of Machine
With single Hooke's joint it is possible to connect two shafts, the axes of which have an angular misalignment up to

30°
40°
10°
20°

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

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Theory of Machine
Maximum fluctuation of energy in a flywheel is equal to [where I = Mass moment of inertia of the flywheel, E = Maximum fluctuation of energy, CS = Coefficient of fluctuation of speed, and ω = Mean angular speed = (ω₁ + ω₂)/2]

I.ω².CS
I.ω.(ω₁ - ω₂)
All of these
2.E.CS

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