Theory of Machine
A machine mounted on a single coil spring has a period of free vibration of tp . If the spring is cut into four equal parts and placed in parallel and the machine is mounted on them, then the period of free vibration of the new system will become

tp /16
tp /4
4 tp
16 tp

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Theory of Machine
The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r₁ = Minimum radius of the cam, r₂ = Radius of the roller follower, and θ = Angle turned by the cam from the beginning of the follower displacement)

(r₁ - r₂) (1 - cosθ)
(r₁ + r₂) (1 + cosθ)
(r₁ + r₂) [(1 - cosθ)/cosθ]
(r₁ - r₂) [(1 - cosθ)/cosθ]

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