Theory of Machine
The natural frequency of free longitudinal vibrations is equal to (where m = Mass of the body, s = Stiffness of the body, and δ = Static deflection of the body)

1/2π × √(s/m)
Any one of the listed here
0.4985/√δ
1/2π × √(g/δ)

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Theory of Machine
Kinematic pairs are those which have

Elements of pairs not held together mechanically
Point or line contact between the two elements when in motion
Two elements that permit relative motion
Surface contact between the two elements when in motion

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Theory of Machine
In a steam engine, one method of obtaining the earlier cut-off with a simple slide valve is by increasing the angle of advance of the eccentric while the throw of the eccentric, steam lap and exhaust lap are kept constant. This method will

Reduce length of effective stroke of piston
Cause withdrawing or throttling of steam
Reduce maximum opening of port to steam
All of these

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