how did galileo know that the pendulum swings at the same frequency
regardless of the amplitude?

note: since pendulum were crucial to the building of the first clocks,
galileo couldn't have used a clock to find the answer.

"francisco" wrote in message
.. .
how did galileo know that the pendulum swings at the same frequency
regardless of the amplitude?

note: since pendulum were crucial to the building of the first clocks,
galileo couldn't have used a clock to find the answer.

He could compare two or more pendulums of equal length but different
amplitude.

On Sun, 28 Aug 2005 03:05:51 GMT, "francisco"
wrote:

how did galileo know that the pendulum swings at the same frequency
regardless of the amplitude?

note: since pendulum were crucial to the building of the first clocks,
galileo couldn't have used a clock to find the answer.

I believe that he used his pulse. Not very precise, but better than
nothing.

the softrat
Sometimes I get so tired of the taste of my own toes.

--
He's about as subtle as a chainsaw, but lacking the social grace.

In article ,
says...
On Sun, 28 Aug 2005 03:05:51 GMT, "francisco"
wrote:

how did galileo know that the pendulum swings at the same frequency
regardless of the amplitude?

note: since pendulum were crucial to the building of the first clocks,
galileo couldn't have used a clock to find the answer.

I believe that he used his pulse. Not very precise, but better than
nothing.

I read an article which stated that Galileo was a fine singer and he
used his music to determine the time.



the softrat
Sometimes I get so tired of the taste of my own toes.

--
He's about as subtle as a chainsaw, but lacking the social grace.




--
Ask yourself, what would God think of your ideals, religion and beliefs?

Observations of Bernard - No 83

"John Zinni" wrote in message
...
| "francisco" wrote in message
| .. .
| how did galileo know that the pendulum swings at the same frequency
| regardless of the amplitude?
|
| note: since pendulum were crucial to the building of the first
clocks,
| galileo couldn't have used a clock to find the answer.
|
| He could compare two or more pendulums of equal length but different
| amplitude.
|
Good Grief! Why don't you guess the answer instead of finding out?

In the 1600's everyone went to church, including Galileo Galilei.
This filled the churches.
The people stank, and incense was burned to mask the odour.


Etymology: Middle English encens, from Old French, from Late Latin
incensum, from Latin, neuter of incensus, past participle of incendere
to set on fire, from in- + -cendere to burn; akin to Latin candEre to
glow -- more at CANDID
1 : material used to produce a fragrant odor when burned
2 : the perfume exhaled from some spices and gums when burned; broadly :
a pleasing scent

To distribute the pong of burning incense, the incense pot was hung
from the church roof by a long rope or chain and swung back and forth.

Galileo, intelligent, sitting in church and bored with the repetitive
proceedings, timed the swing of the pot by counting his own pulse.

Androcles.

"Androcles" Androcles@ MyPlace.org wrote in message
...

"John Zinni" wrote in message
...
| "francisco" wrote in message
| .. .
| how did galileo know that the pendulum swings at the same frequency
| regardless of the amplitude?
|
| note: since pendulum were crucial to the building of the first
clocks,
| galileo couldn't have used a clock to find the answer.
|
| He could compare two or more pendulums of equal length but different
| amplitude.
|
Good Grief! Why don't you guess the answer instead of finding out?

In the 1600's everyone went to church, including Galileo Galilei.
This filled the churches.
The people stank, and incense was burned to mask the odour.


Etymology: Middle English encens, from Old French, from Late Latin
incensum, from Latin, neuter of incensus, past participle of incendere
to set on fire, from in- + -cendere to burn; akin to Latin candEre to
glow -- more at CANDID
1 : material used to produce a fragrant odor when burned
2 : the perfume exhaled from some spices and gums when burned; broadly :
a pleasing scent

To distribute the pong of burning incense, the incense pot was hung
from the church roof by a long rope or chain and swung back and forth.

Galileo, intelligent, sitting in church and bored with the repetitive
proceedings, timed the swing of the pot by counting his own pulse.

I seriously doubt that Galileo conducted all of his pendulum experiments
while bored out of his skull sitting in church.

On Sun, 28 Aug 2005 03:05:51 GMT, "francisco"
wrote:

how did galileo know that the pendulum swings at the same frequency
regardless of the amplitude?

note: since pendulum were crucial to the building of the first clocks,
galileo couldn't have used a clock to find the answer.

A pendulum is slower at larger amplitudes.
John Polasek
http://www.dualspace.net

"francisco" writes:

how did galileo know that the pendulum swings at the same frequency
regardless of the amplitude?

Strictly speaking, this is not true. The frequency does change with the
amplitude. For small amplitudes, the deviation of the frequency from its
limiting value as the amplitude approaches zero (i.e. sqrt(g/l), where
the length of the pendulum is l) is quadratic in the amplitude. This
means that, for small amplitudes, the deviation of the frequency from
sqrt(g/l) is very small, and can be discounted for practical purposes.

So the frequency is, for all *practical* purposes, effectively constant
over a range of amplitudes from 0 up to a point where the variation of the
frequency becomes large enough that it can no longer be ignored.

-----

"John Zinni" wrote in message
...
| "Androcles" Androcles@ MyPlace.org wrote in message
| ...
|
| "John Zinni" wrote in message
| ...
| | "francisco" wrote in message
| | .. .
| | how did galileo know that the pendulum swings at the same
frequency
| | regardless of the amplitude?
| |
| | note: since pendulum were crucial to the building of the first
| clocks,
| | galileo couldn't have used a clock to find the answer.
| |
| | He could compare two or more pendulums of equal length but
different
| | amplitude.
| |
| Good Grief! Why don't you guess the answer instead of finding out?
|
| In the 1600's everyone went to church, including Galileo Galilei.
| This filled the churches.
| The people stank, and incense was burned to mask the odour.
|
|
| Etymology: Middle English encens, from Old French, from Late Latin
| incensum, from Latin, neuter of incensus, past participle of
incendere
| to set on fire, from in- + -cendere to burn; akin to Latin candEre
to
| glow -- more at CANDID
| 1 : material used to produce a fragrant odor when burned
| 2 : the perfume exhaled from some spices and gums when burned;
broadly :
| a pleasing scent
|
| To distribute the pong of burning incense, the incense pot was hung
| from the church roof by a long rope or chain and swung back and
forth.
|
| Galileo, intelligent, sitting in church and bored with the
repetitive
| proceedings, timed the swing of the pot by counting his own pulse.
|
| I seriously doubt that Galileo conducted all of his pendulum
experiments
| while bored out of his skull sitting in church.

You can seriously doubt all you want, but it was the biggest pendulum
handy. Churches were the largest buildings around in the 17th century,
topped only by cathedrals and the Coliseum which didn't have a roof
to hang a pendulum from. Slow pulse, no pocket watch, he needed a
long swing to time as best he could.
What do you think he used, a car tyre on a rope hanging from a tree
with a kid swinging on it?

Androcles

"Androcles" Androcles@ MyPlace.org wrote in message
k...

"John Zinni" wrote in message
...
| "Androcles" Androcles@ MyPlace.org wrote in message
| ...
|
| "John Zinni" wrote in message
| ...
| | "francisco" wrote in message
| | .. .
| | how did galileo know that the pendulum swings at the same
frequency
| | regardless of the amplitude?
| |
| | note: since pendulum were crucial to the building of the first
| clocks,
| | galileo couldn't have used a clock to find the answer.
| |
| | He could compare two or more pendulums of equal length but
different
| | amplitude.
| |
| Good Grief! Why don't you guess the answer instead of finding out?
|
| In the 1600's everyone went to church, including Galileo Galilei.
| This filled the churches.
| The people stank, and incense was burned to mask the odour.
|
|
| Etymology: Middle English encens, from Old French, from Late Latin
| incensum, from Latin, neuter of incensus, past participle of
incendere
| to set on fire, from in- + -cendere to burn; akin to Latin candEre
to
| glow -- more at CANDID
| 1 : material used to produce a fragrant odor when burned
| 2 : the perfume exhaled from some spices and gums when burned;
broadly :
| a pleasing scent
|
| To distribute the pong of burning incense, the incense pot was hung
| from the church roof by a long rope or chain and swung back and
forth.
|
| Galileo, intelligent, sitting in church and bored with the
repetitive
| proceedings, timed the swing of the pot by counting his own pulse.
|
| I seriously doubt that Galileo conducted all of his pendulum
experiments
| while bored out of his skull sitting in church.

You can seriously doubt all you want, but it was the biggest pendulum
handy. Churches were the largest buildings around in the 17th century,
topped only by cathedrals and the Coliseum which didn't have a roof
to hang a pendulum from.

And this is relevant why??? You don't need the largest building around to
conduct a few simple pendulum experiments.

"Time measurement was a major issue in many of Galileo's experiments. For
his pendulum experiments, Galileo seems to have compared the pendulums in
pairs over the same time. For example, a person would be assigned to each
pendulum of the pair and between the words "start" and "stop" each person
would count the number of oscillations. This method was used for comparison
in these experiments."
http://galileo.rice.edu/lib/student_..._pendulum.html



Slow pulse, no pocket watch, he needed a
long swing to time as best he could.
What do you think he used, a car tyre on a rope hanging from a tree
with a kid swinging on it?

Androcles