A simple pendulum starts oscillating simple harmonically from its mean position ( x =0 ) with amplitude ' a ' and periodic time ' T '. The magnitude of velocity of pendulum at X= a 2 is

Step-by-step solution

The velocity in simple harmonic motion is given by v = a^2 - x^2 , where = 2 T is the angular frequency. At displacement x = a 2 , the velocity becomes: v = 2 T a^2 - ( a 2 )^2 = 2 T a^2 - a^2 4 = 2 T 3a^2 4 = 2 T 3 a 2 = 3 a T This corresponds to option D .