A simple pendulum oscillates with an angular amplitude . If the maximum tension in the string is twice the minimum tension then is

Step-by-step solution

Let the mass of the bob be m and the length of the string be l . At any angle , the tension T in the string 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 ( - ) mv^2 l = 2mg ( - ) Substituting this into the tension equation, we get: T = mg + 2mg ( - ) = mg (3 - 2 ) The maximum tension occurs at the lowest point ( = 0 ): T_ = mg (3 - 2 ) The minimum tension occurs at the extreme positions ( = ): T_ = mg (3 - 2 ) = mg Given that T_ = 2 T_ : mg (3 - 2 ) =