Theory of Machine
The length of a simple pendulum which gives the same frequency as the compound pendulum, is

kG + l₁
(kG² + l₁²)/ l₁
kG² + l₁
(kG + l₁²)/ l₁

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Theory of Machine
The relation l = (2/3).(j + 2) apply only to kinematic chains in which lower pairs are used. This may be used to kinematic chains in which higher pairs are used, but each higher pair may be taken as equivalent to

Two lower pairs and two additional links
Any one of these
One lower pair and two additional links
Two lower pairs and one additional link

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