Theory of Machine
The velocity of a particle moving with simple harmonic motion, at any instant is given by (where ω = Displacement of the particle from mean position)

ω √(x² - r²)
ω² √(x² - r²)
ω √(r² - x²)
ω² √(r² - x²)

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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

l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³
(l₁ + l₂ + l₃)/3
l₁ + l₂ + l₃

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Theory of Machine
A thin circular disc is rolling with a uniform linear speed, along a straight path on a plane surface. Which of the following statement is correct in this regard?

The centre of the disc has zero acceleration
The point on the disc making contact with the plane surface has zero acceleration
The centre of the disc has centrifugal acceleration
All points of the disc have the same velocity

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