A pendulum, like one in a grandfather clock, accelerates and decelerates at a constant rate because of gravity. What causes the arc of the pendulum to decrease is the natural resistance the pendulum encounters because of air resistance. The effects of air resistance can be experienced every day simply by trying to walk into a headwind, for example. It is this same force that has an effect on any scientific experiments using pendulums.
Famous scientist Galileo Galilei conducted some of the most extensive experiments on pendulums and eventually discredited theories from Greek scientist Aristotle. He noted that the length of the arc had almost no effect on how long the pendulum took to complete a full oscillation, or the time it takes for the pendulum to return to its original position. He conducted an experiment where two pendulums were released, one from 5 degrees and the other from 45 degrees. The oscillation periods of both were about 30 seconds. This result allowed him to discredit the theory that a heavier object falls faster than does a lighter one. The combination of these two observances means that only air resistance affects falling objects and pendulums.
Friction exists all around us. Cars will naturally slow down if no gas is applied, as the tires and aerodynamics of the vehicle will eventually cause the speed to reach zero. The same is true of pendulums travelling through the air. It is easy to think the air offers no resistance, as people can walk through air with no difficulty, but this is not true. The atoms making up the air -- oxygen, carbon dioxide, nitrogen, hydrogen and helium -- all have physical structures and so exert forces back.
The effect of air resistance on a pendulum is called damping, where the length of the arc is decreased by the force of the air, although has no effect on the oscillation period, as noted by Galileo. The nature of the experiment dictates how much of an effect damping has. For anything that has real-world applications, air resistance is an important factor and needs to be taken into account. To get around air resistance in experiments, allow the pendulum to complete only one oscillation at a time. During the first swing, air resistance will have only a negligible effect on the pendulum.
To reduce the effects of air resistance even more, use streamlined pendulums. The concept of car aerodynamics is well known. Race cars have no sharp edges and are streamlined to reduce the drag effect from the air. The same is true of pendulums. A thin rod and a spherical bob, or weight, will be affected less by air resistance than will a coarse string and a square bob. This tendency is why the pendulums in efficient grandfather clocks are very thin in profile.
In a vacuum, there is no air and, thus, no air resistance. If a pendulum were set swinging in a vacuum, it would never stop and, in fact, would maintain a constant arc in terms of time and distance.
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