A pendulum consists of a mass, called a bob, that is affixed to the end of a string of length L (see Figure 6.24). When the bob is moved from its rest position and released, it swings back and forth. The time it takes the pendulum to swing from its farthest right position to its farthest left position and back to its next farthest right position is called the period of the pendulum.
Figure 6.24

Let θ = θ(t) be the angle of the pendulum from the vertical. It can be shown that if there is no resistance, then when e is small it satisfies the differential equation
θ n + g/L θ = 0
where g is the constant of acceleration due to gravity, approximately 9.7 m/s2. Suppose that L = 1 m and that the pendulum is at rest (i.e., e = 0) at time t = 0 second. The bob is then drawn to the right at an angle of θ1 radians and released.
(a) Find the period of the pendulum.
(b) Does the period depend on the angle 81 at which the pendulum is released? This question was posed and answered by Galileo in 1 638. [Galileo Galilei (1 564- 1642) studied medicine as a student at the University of Pisa, but his real interest was always mathematics. In 1 592, Galileo was appointed professor of mathematics at the U niversity of Padua in Venice, where he taught primarily geometry and astronomy. He was the first to use a telescope to look at the stars and planets, and in so doing, he produced experimental data in support of the Copernican view that the planets revolve around the sun and not the earth. For this, Galileo was summoned before the Inquisition, placed under house arrest, and forbidden to publish his results. While under house arrest, he was able to write up his research on falling objects and pendulums. His notes were smuggled out of Italy and published as Discourses on Two New Sciences in 1 638.]