## THE PENDULUM

What is the mechanism which drives the pendulum? Why did Galileo use a pendulum? Was he right? Did his conclusions influence science? Have other instruments been developed on the same technological basis?

The pendulum is assembled from a string or a light rod with a weight at one end.Galileowas the first to examine its unique characteristics. Galileo found that each pendulum has a constant period. The period is the time in which a pendulum completes a single oscillation, i.e., returns to the position it was in at the beginning of the period. For example: The time required for the pendulum to move from its most extreme right position back to that point. The pendulum passes twice through the arc during each period.

Go to the Laboratory

Why did Galileo become interested in pendulums? How did he hit on the idea that pendulums have a constant period?

## Why did Galileo become interested in pendulums?

How did he hit on the idea that pendulums have

a constant period?Viviani, Galileo's pupil,wrote that Galileo observed the motions of a chandelier hanging in a cathedral and noticed that it has a constant period even when moving at different angles.

Vivianiclaims that was how he discovered the laws of pendulum motion. According to other conjecture Galileo noticed the qualities of different musical instruments (his father was a musician) and that he discovered the properties of the pendulum through his experience and activities in the area of music.

In 1602Galileo began conducting experiments with pendulums in order to examine:If their periods are indeed constant?In order to determine the exact period of the pendulum, one must count the number of oscillations within a specified time. Galileo and his students measured the number of oscillations through which a pendulum passes in an entire day, in order to determine its precise period. Following the success of these experiments, Galileo claimed that the pendulum has a constant period. In light of this conclusion, he began to use the pendulum to measure short time periods ( in his

inclined planeexperiments for example ), although it was still less precise than thewater clock. Galileo examined a variety of pendulums and claimed that the period of each is totally independent of the size of the arc through which it passes. A pendulum with an angle of 80 degrees has an identical period to that of a pendulum with an angle of 2 degrees.

Today we know that the period of the pendulum will remain constant as long as the pendulum's angle is no greater than about 20 degrees, and even then, it is not completely precise. A pendulum moving along a greater arc traverses a greater distance and its velocity is greater, for it falls from a greater height and at a more acute angle. As a result of these factors, its speed is far greater. The surprising conclusion - the pendulum traverses a longer distance in a shorter time, than in a shorter distance, and its period is shorter.

## Was Galileo right in his assumption that

the period of a pendulum is constant?

for the ball to fall?

There are a number of reasons why Galileo thought that the period remains constant.

- One factor which Galileo failed to consider is friction. All of the experiments were conducted in air and the factor of friction was thus present in all of them. This friction slowed down the pendulum's faster movements and led to a decrease in the length of the arc through which it passed. For example: If you move a pendulum to an angle of 60 degrees, within a short number of cycles the pendulum will not extend beyond an angle of 20 degrees because of the friction. Because Galileo measured a large number of cycles, he thought that this law held true for larger angles too.
- Galileo discovered that the periods of smaller angles were constant and assumed that this was correct for every angle, an assumption which we now know to be wrong.
Galileo tried to prove on the basis ofthe law of fallthat the period of a pendulum is constant, i.e., that the time required for the pendulum to fall from its highest to its lowest point is constant, but he did not succeed in doing so. This failure did not prevent him from continuing to consider validity this law, which was discovered through experimentation. It is interesting that Galileo succeeded in proving the correct law, according to which the time required for the descent onto the straight lines connecting the ends of the pendulum's movement (the chords in the circle marked in the drawing) is constant, and does not depend on the angle of the pendulum's inclination. However, this law is only correct for movement along the straight chords, and not for the circular movement which the pendulum describes. Note that for small angles, the straight line is almost identical to the circle, so that the descent period is constant for the circle too. For this reason, the period of the pendulum at small angles is constant. Galileo also proved that movement along the arc is always faster than movement along the straight lines (the chords), but continued to hold the assumption that the period of pendulums is always constant.

## The pendulum's influence on science.

The pendulum demonstrates a continuous perpetual motion - or, to be precise, almost perpetual - until it stops because of friction. Continuous motion was compatible with the new17th centuryphysics and incompatible with thephysics of Aristotle. The explanation for the pendulum's motion is related to Galileo'sprinciple of inertiaandthe law of fall, which serve as the basis of the new physics. The motion of the pendulum is one of falling, but it does not fall at a constant acceleration because the angle of its descent changes along the length of each movement. The acceleration of the falling body can serve as an example for those who accept theprinciple of inertia.

## The pendulum's influence on technology.

Galileo began measuring time with the pendulum, but it could only be used as a stop watch at most, by counting its oscillations over a given period. In order to measure longer time units it was necessary to sit in front of the pendulum all day and count its oscillations in order to calculate the time - a method which is neither efficient nor practical. An additional problem was the stopping of the pendulum because of air friction. We like our clocks to continue working for days and not to stop after a short time.

Galileo began building a clock based on the pendulum's precise measurement of time, but he was confronted by two problems:

- The difficulty of transferring the energy (transmission) from the pendulum's oscillations to a cog-wheel, which would eventually move the dials. Galileo attempted to connect a rod pendulum in such a way that the rod would push the cog-wheel at every cycle. However, this rod only transferred part of the pendulum's movement (i.e., part of the amount of speed) to the cog-wheel, thus increasing the second problem.
- The problem of the pendulum's movement stopping as a result of air friction.
Galileo failed to build a clock based on the principle of the pendulum, butin 1657 Christian Huygens of the Netherlands, who was involved in physical and mathematical research, produced the first pendulum clock based on this technology. Huygens' clock was many times more precise than any of the clocks produced before. The pendulum clock's mechanism was large in order to keep it precise. Over the years, the pendulum clock was perfected by many researchers on the basis of the same principle. Up to the beginning of the twentieth century, pendulum clocks were the most precise clocks available. In city squares of large cities, clock towers were built, some of which are still working, such as Big Ben in London. Smaller clocks were introduced into the homes of the rich. Over the years, pendulum clocks penetrated many homes -- even today one can find antique pendulum clocks in many homes, and new pendulum clocks are still being manufactured.

Experiment 1:Which pendulum has a shorter period, a pendulum with an angle of twenty degrees or a pendulum with an angle of 5 degrees?

conclusions:The time required for the pendulum to complete a 20 degree arch will be identical to the time required to complete a 5 degree arch.

Experiment 2:Go to the laboratory and try to change the length of the pendulum, its weight and the material from which it is made. What is the factor which influences the period? And to what extent?

Build your own personal pendulum:

Material: iron/wood/plastic

Length: 3cm/8cm/30cm

Weight: 10 grams/250 grams/1 kg

conclusions:Galileo also noticed that the period of the pendulum is not dependent on the material from which it is made or on its weight. The pendulum's period is influenced by its length alone. The longer the pendulum, the longer its period.

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