In the string of an oscillating pendulum, the maximum tension is double the minimum tension. Determine the angular amplitude.

Step-by-step solution

Let the angular amplitude be ₀ . The tension in the string at an angle with the vertical is given by T = mg + mv^2 l . By conservation of energy, the velocity v at angle is given by 1 2 m v^2 = mg l ( - ₀) , which gives v^2 = 2gl ( - ₀) . Substituting v^2 into the tension equation, we get T = mg + 2mg ( - ₀) = mg (3 - 2 ₀) . The maximum tension occurs at the lowest point ( = 0 ): T_ = mg (3 - 2 ₀) The minimum tension occurs at the extreme position ( = ₀ ): T_ = mg (3 ₀ - 2 ₀) = mg ₀ Given that T_ = 2 T_ : mg (3 - 2