All,

I'm confused by the recent messages that imply that a pendulum with a LIGO X-
suspension should be designed with the center of mass above the platform 
suspended by the crossed flexures. 

In this scheme one end of each of 4 flexures (wires or shim stock strips) are rigidly 
supported.  (These supports make a rectangle in the the horizontal plane.)  The other 
ends of the flexures are connected to, and support, a platform so that the flexures 
make an X when viewed from the side.  The supported platform is the top of the 
moving part of the pendulum.

This scheme is well described in the paper written by Barton and Kuroda, Ultralow 
Frequency Oscillator,  Rev. Sci. Instrum. 65 (12), Dec. 1994.  It explains that for a 
particular suspension geometry there is a critical vertical position.  If the CoM is 
below the critical position the pendulum is stable - if the CoM is above it is unstable.  
As the CoM approaches the critical position from below the pendulum period 
becomes arbitrarily large.  Under most practical circumstances the critical position is 
below the suspended platform.

My limited experiments with a LIGO X-suspension are consistent with Barton and 
Kuroda's description.


Chuck Burch
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