"John Zinni" wrote in message
...
| "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.

You do if you don't have a watch with a second hand on it.



| "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

That came later, when he wanted to refine his initial discovery.

|
|
| 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
|
|
|
|
|

i found the following article about the law of the pendulum and galileo in
http://equinox.unr.edu/homepage/nick...rs/galileo.htm

The law of the pendulum. According to a story that is probably not true,
during a particularly boring mass in the Pisa Cathedral (a beautiful
building that still exists, next to the famous Leaning Tower), Galileo
noticed that an overhead lamp, hanging from a long chain, swung back and
forth at regular intervals. He timed the oscillations against his pulse and
determined that they were remarkably regular. Later, he was able to
formulate pendular motion with mathematical precision. Today, we write the
law of the simple pendulum thus: T = 2p ./ (L/g). In words, the period of
time T required to complete a whole swing back to the starting point, equals
2 pi (= 6.28), times the square root of the length L of the pendulum divided
by the acceleration g due to gravity (which is 32 feet per second per
second). We now know that this "law" holds only approximately, when the
pendulum swing is not too big. This law of the simple pendulum describes one
form of "simple harmonic motion," one of the most fundamental phenomena of
physics. The laws of simple harmonic motion are one key to the development
of every single branch of physics, including theory of heat, light, and
electromagnetic phenomena. For example, a mass oscillating up and down on a
spring exhibits simple harmonic motion, and the "sine wave" familiar from
electronics, is yet another form of simple harmonic motion. Imagine that the
mass on a spring is a pen. If graph paper moves steadily by, the moving pen
inscribes the uniformly wavy line of the sine and cosine curves. Slam your
fist into a table top and, to a first approximation, you set it into a
damped harmonic vibration.
Some other modern formulas are x = A cos wt = A cos 2pft = A cos ./(k / m)
t, where x is position on the x-axis, w is angular frequency or radian
frequency, t is time (as represented by position on the t axis), A is
amplitude of the oscillation, f is frequency of vibration, k represents the
stiffness of an oscillating spring, m is the mass of the bob on the end of
the spring or pendulum, and ./ is the square-root symbol.

The theory of simple harmonic motion (which achieved its modern development
after Galileo) is a good example of a paradigmatic scientific achievement
that provides the basis of a common description and explanation of a wide
variety of seemingly unrelated phenomena. It holds whenever there is a
restoring force F proportional to the distance x that something is
displaced, F = - kx, such as a stretched rubber band or a marble moved up
the side of a round bowl.

In Galileo's day, the law of the pendulum was crucial to developing accurate
pendulum clocks. The point is that, in the range of swings that are not too
large, the period (or frequency) of the oscillations is independent of the
exact size (amplitude) of the swing. Thus, as the clock winds down and the
swings get smaller, the pendulum still beats at the same rate. It was the
Dutch mathematician and natural philosopher, Christian Huygens, who actually
developed good pendulum clocks, after Galileo's death. Clocks were typically
driven by weights, but spring-driven clocks also underwent rapid development
in the 17th century.

"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.

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

"John Zinni" wrote in message
...
| "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.

You do if you don't have a watch with a second hand on it.



| "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

That came later, when he wanted to refine his initial discovery.

I would phrase it ...

That came later, when he wanted to verify his initial suspicion.


Counting the number of oscillations in a given period of time as judged by
his pulse is fine while he was sitting bored in church, but comparing the
number of oscillations of two pendula in some arbitrary period of time is a
controlled experiment.



|
|
| 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
|
|
|
|
|

He used his heart beat.

"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.

In fact the period of a simple pendulum does vary with amplitute and for big
amplitudes the error is noticable. His theory is only true for small
amplitudes relative to their length.

Hi.

Chris.

"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.

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.

He used his pulse.

Bob Kolker

francisco wrote:


In Galileo's day, the law of the pendulum was crucial to developing accurate
pendulum clocks. The point is that, in the range of swings that are not too
large, the period (or frequency) of the oscillations is independent of the
exact size (amplitude) of the swing. Thus, as the clock winds down and the
swings get smaller, the pendulum still beats at the same rate. It was the
Dutch mathematician and natural philosopher, Christian Huygens, who actually
developed good pendulum clocks, after Galileo's death. Clocks were typically
driven by weights, but spring-driven clocks also underwent rapid development
in the 17th century.

It is ironic that constant frequency of pendula of a given length could
be used to prove that the Earth indeed moves (i.e. rotates). Leon
Focault did just that in 1851. If Galileo fully grasped inertia he might
have thought of that experiment well before Focault.

If you recall the scholars of the Church faulted Galileo for failing to
prove the motion(s) of the Earth. He assumed the motions and thought the
tides were sufficient proof. It turned out Galileo's theory of tides was
flat out wrong and did not constitute proof of the earth's motion(s).
Stellar Aberration was not known until 1726 and Focault's Pendulum was
not deployed until 1851. The motion(s) of the earth were supposed or
hypothesized prior to be being emprically established. By the time
Focault deployed his epynomous pendulum most of the world accept the
motion(s) of the earth as being obvious or commonsensical. They were
neither.

Bob Kolker

Androcles:

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?

I guess that depends upon whether or nottheroads were so bad that
he had lots of ruined tyres from which to make swings (and rope of
course - but I'm pretty sure they had trees back then).

(David McAnally) writes:

"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.

Incidentally, this is angular frequency, so it is measured in radians per
unit time, and not cycles per unit time.

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.

Note that the time evolution of the pendulum is expressible in terms of
Jacobi elliptic functions.

-----

Bob Kolker: Liked your posts re the motions of the earth. It is a
great story in itself how mankind went from unanimous belief in the
unmoving flat earth, to broad acceptance that the earth was a sphere
spinning in space. We unfortunately take this story for granted, but it
actually involved an incredible amount of discovery and work and pain.

I once owned a little book that I bought on sale for 25 cents. It was
the step by step story how we went from the flat earth to the spinning
sphere. It contained many items that we don't even hear about these
days, and unhappily are not taught our children. For example, if there
were an internet way back then, they would be arguing as to why a ship
coming into harbour had the top of its mast first seen rather than its
main body. IIRC about 20 reasons were given for abandoning the flat
earth in favor of the spinning sphere.
I think that the whole process of belief change was an exciting story
and illustrative as to how science works.