A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical ?

Step-by-step solution

In mean position, aligned T & =3 m g Net force, T-m g & = m v^2 l aligned aligned & 3 m g-m g & m v^2 l v & = 2 g l aligned Let maximum displacement with respect to vertical is , then aligned 1 2 m v^2 & =m g h & =m g(l-l ) 1 2 m(2 g l) & =m g l(1- ) & =0 aligned =90^