Galileo used water flowing from a container to measure time.

His unit of time was a TEMPO.

He investigated the motion of a pendulum during intervals of time. And he considered the relationship between time for pendulum motion and time for free fall motion.

Our present description for a small arc of pendulum motion is:

If "L inches" is the length of the pendulum from the point of attachment to the center of gravity of the object swinging then the period in seconds for one swing across the center line and back, A to B and back to A, is two pie times the square root of the ratio of L divided by 386 (385.8267717) inches per second squared.

So a 9.773106296 inch pendulum takes __________ seconds.

- - - - - - - - - -

A 16 inch pendulum takes __________ seconds.

The frequency in swings per second is the reciprocal of the period.
Galileo's first account of free fall motion was based on the odd integers 1, 3, 5, ...

During equal time intervals successively timed from rest, the speed of a falling object increased by intervals in proportion to the odd integers.

Later, with his study of pendulum motion, he developed an equivalent model to our *s = - 192.9133858 t² * model.

In some algebra classes the series 1 + 3 + 5 + ... + (2n - 1) is investigated.

Show the relationship between this series and *s = - 192.9133858 t²*.
A "Unit Toss" of 16 inches hight takes T = 2(16/192.9133858)^.5 = .575981859 seconds.

Your calculation of the time for a swing of a 16 inch pendulum, equal to 1.279509987 seconds, divided by the time for a "Unit Toss",.575981859 seconds, gives a ratio of 2.221441468. Not all that interesting you say!

Find the product of the square root of two and 2.221441468 = ___________
Galileo's Constant, pi divided by the square root of eight, is discussed on page 10 of Albert DiCanzio's "Galileo: His Science and His Significance for the Future of Man" book, © 1996, where Albert DiCanzio gives credit to Stillman Drake for naming this constant.

##### "Out Juggling In My Class" by William V. Thayer

###### copyright © 1997-8 Wm. V. Thayer, All Rights Reserved

## Juggleometry History

## Pendulum

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