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An examination of the time period for a pendulum

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.

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.

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 of the law of fall that the period of a pendulum is constant, i.

The Time-Period of a Simple Pendulum.

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 chordsbut 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 new 17th century physics and incompatible with the physics of Aristotle.

The explanation for the pendulum's motion is related to Galileo's principle of inertia and the law of fallwhich 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 the principle 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 an examination of the time period for a pendulum. The problem of the pendulum's movement stopping as a result of air friction.

  • This friction slowed down the pendulum's faster movements and led to a decrease in the length of the arc through which it passed;
  • 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.

Galileo failed to build a clock based on the principle of the pendulum, but in 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.

An examination of the time period for a pendulum

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.

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

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: 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.