Overview
The simplest pendulum consists of a weight called a bob suspended from a pivot, allowed to swing freely. Its regular motion illustrates the relationship between gravity and tension. For centuries, pendulums were used in timekeeping and measurement.
Motion of a Pendulum
Suppose a solid pendulum bob is suspended from a cord attached to a pivot point. The bob is enough heavier than the cord that the mass of the cord can be treated as zero, and its size is small enough that its mass can be treated as a single point. At equilibrium, the bob is at rest. If it is moved sideways, it will follow a trajectory from that point back through the equilibrium point to a location at an equal angle to the other side and back again. This is called the period of a pendulum. The bob swings back and forth in harmonic and regular motion as gravity acts upon it. In the early 1600’s, Galileo began to study the motion of pendulums, and noticed that the period of the pendulum depends on the length of the cord, but not upon the weight of the bob.
Pendulum Clocks
Since the pendulum oscillates with regular motion, early scientists and engineers began to use it to keep time in clocks. The first refinement was to limit the trajectory angle to a few degrees, because wide swings made the measurements inaccurate. The optimum length for a pendulum, at almost a meter, allowed the period of swing to be two seconds long, creating a “tick-tock” one second apart. Long, narrow clocks, called grandfather clocks, were built to accommodate the length of the pendulum. By the time of the Industrial Revolution, pendulum clocks were used to keep time in homes and businesses. Innovations were introduced that made them very accurate. They were gradually replaced by quartz clocks and electric clocks in the 20th century.
Foucault Pendulum
The French scientist Foucault suspended a very long pendulum cable from the dome of the Pantheon in Paris in the 1850’s. Rather than merely moving from side to side, the pendulum bob kept the same plane but rotated clockwise, so that it made a full circle in about 32 hours. The precession of the bob is caused by the rotation of the earth. Similar pendulums are exhibited in many cities around the world.
Pendulums in Seismometers
The earliest seismometers also used pendulums, mounted horizontally on a frame rather than vertically. The bob of the pendulum was attached to a stylus to record the movements of the earth, such as in the 1906 San Francisco earthquake. Like pendulum clocks, they were replaced by other types of instruments sensitive to motion.
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