A pendulum consists of a mass, called a bob, that is affixed to the end of a string of length L. 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.Let e = 8(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" + 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., θ = 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 θ1 at which the pendulum is released?
A pendulum consists of a mass, called a bob, that is affixed to the end of a string of length L. 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.Let e = 8(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" + 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., θ = 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 θ1 at which the pendulum is released?
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