Substitution of the proper arithmetic values gives 84 minutes as the period. 
Such a pendulum is variously called an "earth's radius pendulum," an "84 min- 
ute pendulum," a "Schuler pendulum" after Prof. M. Schuler who first discov- 
ered this effect. 
It can be shown that the platform is entirely analogous to such a pendu- 
lum. First of all, we have already demonstrated that its operation results in 
its being always vertical as moved about the earth, just as the Earth's radius 
pendulum. Second, if there is an initial displacement of the platform, while 
standing still, the equation of the system (Equation 3) reduces to: 
- [(? 33 ae —-[ ed - 0 
But if there is no motion @ = 8 and the relation becomes: 
2 
Gyan oan d x 35 +" 
dt? R 
The solution of this differential equation is a sinusoidal rocking motion of the 
platform: 
8 = 0 sin (S. t 
R 
The period of this sine wave is given by: 
T =: 2" PR. 
g 
the same expression as that resulting for an earth's radius pendulum. Note 
that the division by R in the Block Diagram is analogous to the variation of the 
pendulum length. Thus, the platform period is also 84 minutes when R is ad- 
justed to be equal to the earth's radius, and motions result in no vertical error. 
This adjustment of the platform is called "Schuler tuning." The analogy is very 
close and so the platform may be thought of as being attached to a pendulum 
equal in length to the Earth's Radius. 
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