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

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Theory of Machine
In a circular arc cam with roller follower, the acceleration in any position of the lift will depend only upon

Total lift, total angle of lift, minimum radius of cam and cam speed
Radius of circular arc, cam speed, location of centre of circular arc and roller diameter
Total lift, centre of gravity of the cam and cam speed
Mass of cam follower linkage, spring stiffness and cam speed

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