In the 4th century BCE, Aristotle believed that an object's motion depended on the very nature of that object. The pendulum posed a problem for him: why does the mass at the end of the string, when released from a certain height, not travel directly to its natural place at the bottom, but then swing upward again?
Much later, in the 17th century, Galileo discovered the isochronism of pendulum oscillations while watching a chandelier swing in Pisa Cathedral as he sat thoroughly bored during Mass: although the swing gradually diminishes over time, the mass always takes the same amount of time to complete a round trip. Galileo used this observation to formulate a law: a pendulum always retains the same period, which does not depend on its amplitude (the angle through which the string moves away from the vertical).
In fact, Galileo's law holds only when the amplitude is "small". At the time, discrepancies were observed at sea. To calculate latitude, one need only measure the Sun's elevation; to calculate longitude, however, the local time must be compared with a reference time. This raised the problem of carrying a reference time on board—of taking clocks stable enough to keep time.
Constant oscillations
===================================
Still in the 17th century, the Dutch scientist Christiaan Huygens was seeking a more accurate instrument for measuring time for his astronomical observations. In 1656, he invented the pendulum clock. In early 1659, Blaise Pascal answered, under a pseudonym, questions he had himself posed about the cycloid, which he called the roulette. A cycloid is the locus of a point on a circle of radius R rolling without slipping along a line (the valve on a bicycle wheel, for example).
