The amplitude of a particle executing SHM is 3 cm . The displacement at which its kinetic energy will be 25 % more than the potential energy is: ______ cm .

Step-by-step solution

Let x be the displacement at which its kinetic energy will be 25 % more than the potential energy. Given here, A = 3   cm and K E = P E + P E 4 So, K E = 5 4 P E ⇒ 1 2 m ω 2 A 2 - x 2 = 5 4 × 1 2 m ω 2 x 2 ⇒ A 2 - x 2 = 5 4 x 2 ⇒ 9 x 2 4 = A 2 ⇒ x = 2 3 A ∴   x = 2 3 × 3   cm ⇒ x = 2   cm