A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

Step-by-step solution

The formula to calculate the potential energy of the particle executing SHM is given by P = 1 2 m ω 2 x 2       . . . 1 The formula to calculate the kinetic energy of the same particle is given by K = 1 2 m ω 2 A 2 - x 2       . . . 2 Divide equation (1) by equation (2) to obtain the required ratio. P K = 1 2 m ω 2 x 2 1 2 m ω 2 A 2 - x 2 = x 2 A 2 - x 2       . . . 3 Substitute A 2 for x into equation (3) to calculate the required ratio. P K = A 2 2