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Theory of Machine

Theory of Machine
When a body moves with simple harmonic motion, the product of its periodic time and frequency is equal to

π/2
π
One
Zero

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Theory of Machine
A disturbing mass m₁ attached to the rotating shaft may be balanced by a single mass m₂ attached in the same plane of rotation as that of m₁, such that (where r₁ and r₂ are the radii of rotation of m₁ and m₂ respectively)

None of these
m₁ r₂ = m₂ r₁
m₁ r₁ = m₂ r₂
m₁ m₂ = r₁ r₂

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Theory of Machine
The equation of motion for a vibrating system with viscous damping is (d²x/dt²) + (c/m). (dx/dt) + (s/m). x = 0. If the roots of this equation are real, then the system will be

Critically damped
Under damped
Without vibrations
Over-damped

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Theory of Machine
The essential condition of placing the two masses, so that the system becomes dynamically equivalent, is (where l₁ and l₂ = Distance of two masses from the centre of gravity of the body, and kG = Radius of gyration of the body)

l₁l₂ = kG²
l₁ = kG
l₁l₂ = kG
l₂ = kG

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Theory of Machine
A ball and a socket forms a

Turning pair
Screw pair
Rolling pair
Spherical pair

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Theory of Machine
The unbalanced primary forces in a reciprocating engine are

Balanced by secondary forces
Not balanced
Balanced partially
Balanced completely

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