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Re: [Phys-l] "compound" pendulum



The usual formula for the period of a physical pendulum is:

T = 2 * pi * sqrt(I/mgd)

where m is the total mass, I is the moment of inertia about the pivot, and d is the distance from the pivot to the center of mass.

For the case described here we have:

I = m1*L1^2 + m2*L2^2
md = abs(m1*L1 - m2*L2).

(Note that if d=0 then the period is infinite, because the gravitational torques on the two end masses then balance at any angle of rotation.)

Define the ratio I/md to be an effective length L. If you now construct a simple pendulum consisting of a point bob of mass m at the end of a light string of length L, it will have exactly the same period as Jeglinski's physical pendulum. For example, if one of the masses or lengths is zero, Jeglinski's pendulum is in fact a simple pendulum. -Carl