The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy is 25% more than its potential energy is ______ cm.
Physics · Circular Motion
JEE Mains 1 February 2023 Shift 1 Morning Shift

Question

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

G1 Physics · Accepted Answer

Given K = 1.25U = (5/4)U. For SHM, K = (1/2)mω²(A²−x²) and U = (1/2)mω²x². Thus A²−x² = (5/4)x², so A²=(9/4)x² and x=(2/3)A=2 cm.