The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement ( x ) starting from mean position to extreme position ( A ) is given by

Step-by-step solution

The formula to calculate the kinetic energy of a particle executing SHM is given by K = 1 2 m ω 2 A 2 - x 2 . . . 1 Substitute 0 for x into equation (1) to obtain the kinetic energy at the mean position. K = 1 2 m ω 2 A 2 - 0 2 = 1 2 m ω 2 A 2 Substitute A for x into equation (1) to obtain the kinetic energy at the end points. K = 1 2 m ω 2 A 2 - A 2 = 0 Hence, the variation can be shown as follows-