Pendulum for celestial rhythms
For a given length from the suspension to the center of gravity, a pendulum swings back and forth at a given frequency (frequency per unit time).
Regardless of whether the pendulum swing is wide or small, the frequency of the back-and-forth swing is always the same for a given length.
The longer a pendulum is, the lower the frequency with which it swings back and forth.
The formula for calculating the so-called mathematical pendulum (string pendulum) was discovered by the Italian scientist Galileo Galilei after he observed the movements of the lamps hung there in different lengths in a church.
He recognized the connection of gravitational acceleration (which is 981 centimeters per second squared on the earth's surface), pendulum length and oscillation time.
A quarter of a pendulum length oscillates with twice the frequency !
The pendulum formula
(from the book "Die Kosmische Oktave" by Hans Cousto):
g = 981 cm . sec -2 = Acceleration due to gravity
L = the length of the pendulum (suspension to the center of mass)
π = 3.14159 Pi
T = Duration of a complete oscillation period (back and forth).
T = 2 . π . √ (l:g) = 2 . π . L -0,5 . g0,5
In our case, T and g are known, and the length L is the quantity we are looking for, so the equation must be solved for L. To do this, the equation is first squared:
T2 = 4 . π2 . L . g-1
This equation is now solved for L:
L = T2 . g . π-2 . 0.25 = T2 . g : (4 . π2)
Any value for T can now be inserted into this equation, whereby the equation can still be transformed expediently beforehand:
L= T2 . g . π-2 . 0.25 = T2 . 24.85 cm . sec-2
Only the time has to be squared and multiplied by 24.85 cm . sec-2 and the result, the pendulum length, is known. However, one can also divide the number 24.85 cm . sec-2 by the square of the frequency f and likewise obtain the desired pendulum length.
The 16th octave of the synodic solar day corresponds to the time:
T = 86400 sec . 2-16 = 1.31836 sec
and the frequency
f = 86400-1 . 216 = 0.7585 Hz
and so the corresponding pendulum length is:
L = 1.318362 sec2 . 24.85 cm . sec-2 = 43.2 cm
L = 24.85 cm . sec-2 . 0.7585-2sec2 = 43.2 cm
In the table "Planets - Sounds - Colors — Meters" the pendulum lengths of the different cycles of the earth, the moon, the planets and the sun are listed.
With a quarter of the pendulum length a pendulum swings back and forth with double frequency, with four times the length with half frequency !
Cosmic Pendulum Mass Tape
to print, cut out and glue (on a cardboard or wooden strip):
Download here as PDF