What should be the displacement of a particle, executing SHM, from its position of equilibrium so that the kinetic energy and the potential energy of the particle are equal?

Explanation

Kinetic energy of a particle executing SHM = `1/2momega^(2)(A^(2)-x^(2))`.
Its potential energy = `1/2momega^(2)x^(2)`.
According to the question,
`1/2momega^(2)(A^(2)-x^(2))=1/2momega^(2)x^(2)or,A^(2)-x^(2)=x^(2)`
or, `2x^(2)=A^(2)or,x^(2)=A^(2)/2`
or, `x=pmA/sqrt2`, this is the required displacement.