Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

(l₁ + l₂ + l₃)/3

l₁ + l₂ + l₃

l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³

l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴

(l₁ + l₂ + l₃)/3

l₁ + l₂ + l₃

l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³

l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴

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Theory of Machine
In vibration isolation system, if ω/ωn < 2, then for all values of damping factor, the transmissibility will be (where ω = Angular speed of the system, ωn = Natural frequency of vibration of the system)

Greater than unity

Less than unity

Equal to unity

Zero

Greater than unity

Less than unity

Equal to unity

Zero

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Theory of Machine
For dynamic balancing of a shaft

The net couple due to the dynamic forces acting on the shaft is equal to zero

Both (A) and (B)

The net dynamic force acting on the shaft is equal to zero

None of these

The net couple due to the dynamic forces acting on the shaft is equal to zero

Both (A) and (B)

The net dynamic force acting on the shaft is equal to zero

None of these

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Theory of Machine
When the relation between the controlling force (Fc) and radius of rotation (r) for a spring controlled governor is Fc = ar + b, then the governor will be

Unstable

Stable

None of these

Isochronous

Unstable

Stable

None of these

Isochronous

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Theory of Machine
The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at

The point on the circumference situated vertically opposite to the contact point

The point of contact

The center of the disc

An infinite distance on the plane surface

The point on the circumference situated vertically opposite to the contact point

The point of contact

The center of the disc

An infinite distance on the plane surface

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Theory of Machine
A shaft has an attached disc at the centre of its length. The disc has its centre of gravity located at a distance of 2 mm from the axis of the shaft. When the shaft is allowed to vibrate in its natural bow-shaped mode, it has a frequency of vibration of 10 rad/s. When the shaft is rotated at 300 r.p.m., it will whirl with a radius of

3.0 mm

2.50 mm

2 mm

2.22 mm

3.0 mm

2.50 mm

2 mm

2.22 mm

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Theory of Machine

Theory of Machine Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

Theory of Machine In vibration isolation system, if ω/ωn < 2, then for all values of damping factor, the transmissibility will be (where ω = Angular speed of the system, ωn = Natural frequency of vibration of the system)

Theory of Machine For dynamic balancing of a shaft

Theory of Machine When the relation between the controlling force (Fc) and radius of rotation (r) for a spring controlled governor is Fc = ar + b, then the governor will be

Theory of Machine The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at

Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

Theory of Machine
In vibration isolation system, if ω/ωn < 2, then for all values of damping factor, the transmissibility will be (where ω = Angular speed of the system, ωn = Natural frequency of vibration of the system)

Theory of Machine
For dynamic balancing of a shaft

Theory of Machine
When the relation between the controlling force (Fc) and radius of rotation (r) for a spring controlled governor is Fc = ar + b, then the governor will be

Theory of Machine
The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at