Work out physical pendulum instantly with clear inputs, formula shown and shareable results.
A rigid body swinging on a pivot has period 2 pi sqrt(I/(mgd)), where d is the pivot-to-centre-of-mass distance. Unlike the simple pendulum, mass distribution matters: I/(md) is the length of a simple pendulum that would keep the same time, which is how a compound pendulum is characterised.
Period
T = 2 pi sqrt(I / (m g d))
Equivalent length
L(eq) = I / (m d)
Because its equivalent length is only two thirds of a metre - the mass is distributed rather than concentrated at the far end.
The point at the equivalent length from the pivot. Striking there produces no reaction at the pivot, which is the sweet spot on a bat.