Consider a pendulum of length L. Let x(t) be the angle the pendulum makes with the

Chapter 9, Problem 33

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Consider a pendulum of length L. Let x(t) be the angle the pendulum makes with the vertical (measured in radians). For small angles, the motion is well approximated by the DEd2x 7?= _g_ LX where g is the acceleration due to gravity (g % 9.81 m/ sec2). How long does the pendulum have to be so that it swings from one extreme position to the other in exactly one second?Historical note: The result of this exercise was considered as a possible definition of the meter. The French committee reforming the measures in the 1790s finally adopted another definition: A meter was set to be the 10,000,000th part of the distance from the North Pole to the Equator, measured along the meridian through Paris. (In 1983 a new definition of the meter was adopted, based on the speed of light.)