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Theory of Machine

Theory of Machine
For an involute gear, the ratio of base circle radius and pitch circle radius is equal to

secφ
sinφ
cosecφ
cosφ

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Theory of Machine
In under damped vibrating system, if x₁ and x₂ are the successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to

log(x₁/x₂)
x₁/x₂
log(x₁.x₂)
loge(x₁/x₂)

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Theory of Machine
When a slider moves on a fixed link having curved surface, their instantaneous centre lies

At the centre of circle
At the centre of curvature
On their point of contact
At the pin joint

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Theory of Machine
The Whitworth quick return motion mechanism is formed in a slider crank chain when the

Smallest link is a fixed link
Slider is a fixed link
Longest link is a fixed link
Coupler link is fixed

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Theory of Machine
If ω/ωn is very low for a body vibrating under steady state vibrations, the phase angle for all values of damping factors, will tend to approach

90°
180°
0°
360°

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Theory of Machine
A single degree of freedom system is given by, m × (d²x/dt²) + c × (dx/dt) + sx = F.cosω.t with usual notations. It represents

Forced vibration with damping
Free vibration with damping
Forced vibration without damping
Free vibration without damping

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