Theory of Machine
A machine mounted on a single coil spring has a period of free vibration of tp . If the spring is cut into four equal parts and placed in parallel and the machine is mounted on them, then the period of free vibration of the new system will become

tp /4
tp /16
16 tp
4 tp

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Theory of Machine
The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the

Unbalanced couples are caused only at higher speeds
Effects of unbalances are proportional to the square of the speed
Unbalanced forces are not dangerous at higher speeds
Effects of unbalances are directly proportional to the speed

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform wear, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3) μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3) μ W (r₁ + r₂)
(1/2) μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2) μ W (r₁ + r₂)

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Theory of Machine
A governor is said to be stable, if the

Radius of rotation of balls increases as the equilibrium speed increases
Radius of rotation of balls decreases as the equilibrium speed increases
Radius of rotation of balls increases as the equilibrium speed decreases
Radius of rotation of balls decreases as the equilibrium speed decreases

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