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 (in cm)

Step-by-step solution

Given amplitude A = 3 cm. The kinetic energy of a particle in SHM is given by K = 1 2 m ^2 (A^2 - x^2) and the potential energy is U = 1 2 m ^2 x^2 . Given that kinetic energy is 25 % more than potential energy: K = U + 25 100 U = 5 4 U 1 2 m ^2 (A^2 - x^2) = 5 4 ( 1 2 m ^2 x^2 ) A^2 - x^2 = 5 4 x^2 A^2 = 9 4 x^2 x = 2 3 A Substituting A = 3 cm: x = 2 3 3 = 2 cm. Answer: 2