Theory of Machine
The driving and driven shafts connected by a Hooke's joint will have equal speeds, if

tanθ = ± cosα
cotθ = cosα
sinθ = ± tanα
cosθ = sinα

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Theory of Machine
A rotor which is balanced statically but not dynamically is supported on two bearings L apart and at high speed of the rotor, reaction on the left bearing is R. The right side of the bearing is shifted to a new position 2L apart from the left bearing. At the same rotor speed, dynamic reaction on the left bearing in the new arrangement will

Become equal to R/2
Remain same as before
Become equal to 2R
Become equal to R/4

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