CALCULATED RESONANT PREQUENCIES OF THE FOUR-LEGGED 
         SUPPORT STRUCTURE FOR THE SECONDARY MIRROR (QUADRUPOD)


                  Calculated    Measured
     Mode          Frequency   Frequency*          Nature of Vibration
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      1             17.2 cps    16.4 cps       Torsional (about optical axis)
      2             33.5        (34            Legs flexing (fundamental)
      3             33.5         34            Legs flexing (different phase)
      4             35.7        (34)           Legs flexing (symmetrical)
      5             48.7      48.6 (to 51)     Torsional (1. overtone) 
      6             59.8         66            Top moves in x direction 
      7             59.8         66            Top moves in y direction 
      8             72.5        73.6           Squatting in z direction?
      9             76.2         93            Top moves in x direction 
     10             76.2         93            Top moves in y direction 
     11             81.9        86.2           Squatting in z direction? 
     12             96.8                       Legs flexing
     13            102.8                       Legs flexing, top fixed
     14            102.8                       Diffn. phasing of mode 13 
     15            108.5                       Torsional, (2. overtone)
     16            185.3                       Legs flexing, top fixed
     17            186.7                       Top displaced
     18            186.7                       Diffn phase of mode 18
     19            194.3                       Top displaced in x
     20            194.3                       Top displaced in y
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 For these calculations, the Z axis is along the optical axis, and the 
 X and Y axes are orthogonal to it, along lines through opposite sets 
 of feet of the quadrupod.  Measurements (*) of the natural frequencies of 
 this structure in the actual telescope by a Modal and Control Dynamics 
 Team at Marshall Space Flight Center founnd the first two torsional modes 
 at 16.4 cps (vs 17.2 in the calculation) and 48.6 cps (vs 48.7).  We have 
 identified the other modes tentatively by sorting through resonances 
 measured for different axes at a point on the side of the top cylinder and 
 at a point on one of the struts.  All these modes result from various ways 
 the four legs bend, as you can see from the plots.  The swaying modes, in 
 which opposing legs shorten and lengthen out of phase, namely modes 6&7 and 
 9&10, are probably shifted to higher frequency because we tensioned the guy 
 wires more than in the calculations.